{"id":2253,"date":"2023-10-02T11:32:46","date_gmt":"2023-10-02T11:32:46","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2253"},"modified":"2023-10-02T11:34:55","modified_gmt":"2023-10-02T11:34:55","slug":"week-8-and-9-ss1-second-term-technical-drawing-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-8-and-9-ss1-second-term-technical-drawing-notes\/","title":{"rendered":"Week 8 and 9 &#8211; SS1 Second Term Technical Drawing Notes"},"content":{"rendered":"<p>\u00a0<br \/>\n\u00a0<strong>WEEK EIGHT-NINE:                                                              DATE:\u2026\u2026\u2026\u2026\u2026\u2026<br \/>\n<\/strong><br \/>\n\u00a0<\/p>\n<h2>Topic:                                                            Equal area of  planefigures<br \/>\n\t<\/h2>\n<p><strong>Content:<br \/>\n<\/strong><\/p>\n<ol>\n<li>Examples on equivalent area of plane figures.<strong><br \/>\n\t\t\t\t<\/strong><\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>Triangles equal in area to  given polygons<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and91.png\" alt=\"\"\/>Example1:  To construct a triangle equal in area to a given polygon with interior angle less than 180<sup>0<\/sup><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Method:<\/p>\n<ol>\n<li>Construct the polygon ABCDE using the given data.\n<\/li>\n<li>Extend the base line AB in both directions.\n<\/li>\n<li>Join DA and DB.\n<\/li>\n<li>Since angle E is opposite to line DA, draw a line from point E parallel to line DA to meet BA extended at point F. Repeat same for point C to get point G.\n<\/li>\n<li>Join DF and DG.\n<\/li>\n<li>Therefore, FGD is the required triangle.\n<\/li>\n<\/ol>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and92.png\" alt=\"\"\/><strong>Example 2<\/strong>   To construct a triangle equal in area to a given polygon with an interior angle greater than<br \/>\n 180<sup>0<\/sup>.<br \/>\nMethod:<br \/>\n(i)        Construct the polygon ABCDE using the given data.<br \/>\n(ii)       Extend the base line AB.<br \/>\n(iii)      Join DA and DB.<br \/>\n(iv)      Since angle E is opposite to line DA, draw a line from<br \/>\npoint E parallel to line DA to meet line AB atpoint F.<br \/>\nSimilarly, from point C draw a line parallel to DB<br \/>\nand this meets AB produced at point G.<br \/>\n(v)      Join DF and DG.<br \/>\n(vi)     Therefore, FGD is the required triangle.<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and93.png\" alt=\"\"\/><strong>Example 3<\/strong> To draw a triangle equal in area to a given regular polygon.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the polygon ABCDEF using the given data.\n<\/li>\n<li>Draw the diagonals of the polygon to intersect at point O.\n<\/li>\n<li>Extend the base line AB in both directions to points P and Q respectively. Where PQ = sum of the length of sides of the polygon ie perimeter of the polygon.\n<\/li>\n<li>Join OP and OQ to obtain the required triangle OPQ .\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A triangle equal in area to a given parallelogram<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and94.png\" alt=\"\"\/><strong>Example 4<\/strong> To construct a triangle equal in area to a given parallelogram.<\/p>\n<p>\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the parallelogram ABCD using the given data.\n<\/li>\n<li>Join point C to A.\n<\/li>\n<li>Draw the base line BA produced.\n<\/li>\n<li>Draw a line from point D parallel to CA and this meets BA produced Point E.\n<\/li>\n<li>Join CE to obtain the required triangle CEB.\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A parallelogram equal in area to a given triangle.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and95.png\" alt=\"\"\/><strong>Example 5:<\/strong>  To draw a parallelogram equal in area to a given triangle.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Draw the triangle ABC using the given data.\n<\/li>\n<li>Draw a perpendicular line from the apex C to meet the base AB at point D.\n<\/li>\n<li>Bisect line CD to get the mid point E.\n<\/li>\n<li>Extend the bisector to both directions to locate point G.\n<\/li>\n<li>Draw a line from point B parallel to AG and this meets the bisector at F.\n<\/li>\n<li>ABFG is the required parallelogram.\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ul>\n<li><strong><em>A triangle equal in area to a given triangle but on a different base<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and96.png\" alt=\"\"\/>Example 6: To construct a triangle equal in area to a given triangle, but having a different base.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the triangle ABC using the given data.\n<\/li>\n<li>Extend the base AB by an amount equal in length to the base of the required triangle ie AD.\n<\/li>\n<li>Join C to D.\n<\/li>\n<li>Draw a line from B parallel to DC and this meets side AC at point E.\n<\/li>\n<li>Join ED. Therefore, ADE is the required triangle.\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A triangle constructed from its known area<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and97.png\" alt=\"\"\/><strong>Example7:<\/strong>  To construct a triangle when given the area.e.g let the given area be 4<sup>1<\/sup>\/<sub>2<\/sub>cm.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Method: <\/p>\n<ul>\n<li>Draw any rectangle ABCD equal to the given area- 3cm x 1<sup>1<\/sup>\/<sub>2<\/sub>cm = 4<sup>1<\/sup>\/<sub>2<\/sub>cm.\n<\/li>\n<li>Draw BC produced and mark off CE equal to BC on it.\n<\/li>\n<li>Draw a line from E to A. Therefore, ABE is the required triangle.\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ul>\n<li><strong><em>A rectangle of different side equal in area to a given rectangle.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and98.png\" alt=\"\"\/><strong>Example 8<\/strong>: To draw a rectangle of different side but equal in area to a given rectangle.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the given rectangle ABCD.\n<\/li>\n<li>Mark off BE on line AB where BE is the required different side.\n<\/li>\n<li> Join EC.\n<\/li>\n<li>Draw line BC produced.\n<\/li>\n<li>Draw a line from A parallel to EC and this meets BC produced at F.\n<\/li>\n<li>FB is the other side of the required rectangle. Complete the required rectangle EBFG.\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A square equal in area to a given rectangle.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and99.png\" alt=\"\"\/><strong>Example 9<\/strong>: To draw a square equal in area to a given rectangle.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the rectangle ABCD using the given data.\n<\/li>\n<li>Draw line AB produced.\n<\/li>\n<li>With B as centre and radius BC, swing an arc to cut AB produced at E.\n<\/li>\n<li>Draw a semicircle on line AE and this cuts line BC produced at F.\n<\/li>\n<li>BF is the length of side of the square.\n<\/li>\n<li>With B as centre and radius BF, swing an arc on line BA to locate point H.\n<\/li>\n<li>With H and F in turn as centres and same radius, locate point G.\n<\/li>\n<li>HBFG is the required square.\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ul>\n<li><strong><em>A rectangle equal in area to a given triangle.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and910.png\" alt=\"\"\/><br \/>\n\t<strong>Example 10:<\/strong>  To draw a rectangle equal in area to a given triangle.<br \/>\n<strong>Method:\u00a0\u00a0\u00a0\u00a0<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the triangle ABC using the given data.\n<\/li>\n<li>\n<div>From the apex C, draw a perpendicular line to\n<\/div>\n<p>meet AB at point D.\n<\/li>\n<li>Bisect line CD to locate the mid point E.\n<\/li>\n<li>Draw a line through point E parallel to Line AB.\n<\/li>\n<li>Erect perpendiculars at points A and B and these\n<\/li>\n<\/ul>\n<p>meet the parallel line through E at points F and G respectively.<\/p>\n<ul>\n<li>ABGF is the required rectangle.\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A square equal in area to a given parallelogram.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and911.png\" alt=\"\"\/><strong>Example 11:<\/strong>  To draw a square equal in area to a given parallelogram.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the given parallelogram ABCD.\n<\/li>\n<li>Draw DA produced.\n<\/li>\n<li>Construct a perpendicular at point A and this cuts CB at F.\n<\/li>\n<li>With A as centre and radius AF, swing an arc to cut DA produced at G.\n<\/li>\n<li>Construct a semicircle on DG and this cut the perpendicular AE at H.\n<\/li>\n<li>AH is the length of side of the required square.\n<\/li>\n<li>With A as centre and radius AH, locate point K.\n<\/li>\n<li>With H and K in turn as centres and same radius AH, locate point J.\n<\/li>\n<li>AKJH is the required square.\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ul>\n<li><strong><em>Division of a triangle into a number of equal areas by parallel lines<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and912.png\" alt=\"\"\/><strong>Example 12:<\/strong>  To divide any triangle in a given number of equal areas eg four (4) by lines<br \/>\ndrawn parallel to one side.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong>(i)   Construct the given triangle ABC.<br \/>\n(ii)  Construct a semicircle on side AC.<br \/>\n(iii) Divide AC into 4 equal parts to produce four (4) equal areas. Three or two parts will produce 3 or 2<br \/>\nequalareas respectively.<br \/>\n(iv) Draw perpendiculars to AC from these 4 divisions and these cuts the semicircle at points F,E and D.<br \/>\n(v)  With C as centre and radius CD, CE and CF in turn, swing arcs to touch AC respectively D1, E1 and<br \/>\nF1.<br \/>\n(vi) Draw lines from these points on AC parallel to line AB. <\/p>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>Division of a triangle into two equal areas by a perpendicular line.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and913.png\" alt=\"\"\/>Example 13: To divide any triangle into two equal areas by a line perpendicular to one side.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Construct the triangle ABC using the given data.\n<\/li>\n<li>Draw a perpendicular line from the vertex C to meet AB at point D.\n<\/li>\n<li>Construct a semicircle on DB.\n<\/li>\n<li>Draw the bisector of line AB and this cut the semicircle at point E.\n<\/li>\n<li>With B as centre and radius BE, swing an arc to cut AB at point F.\n<\/li>\n<li>Draw a line from F parallel to DC and this meets line CB at G.\n<\/li>\n<li>The line FG divides the triangle into two equal areas.\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<strong><em>Division of a triangle into two equal areas by a line drawn from a given point on one side.<\/em><\/strong><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and914.png\" alt=\"\"\/><strong>Example14:<\/strong> To divide any triangle into two equal areas by a line drawn from a given point<br \/>\non one of its sides.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Draw the given triangle ABC indicating the given point P.\n<\/li>\n<li>Draw a line from this point P to connect the vertex C.\n<\/li>\n<li>Bisect line AB to obtain the mid point D.\n<\/li>\n<li>Draw a line from point D parallel to PC and this meets CB at E.\n<\/li>\n<li>Join EP which divides the given triangle into two equal areas.\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A circle of equal area to the sum of two given circles.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and915.png\" alt=\"\"\/><strong>Example 15:<\/strong> To draw a circle equal in area to the sum of two given circles.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ol>\n<li>Draw a line AB equal in length to the diameter of one of the given circles.\n<\/li>\n<li>Draw another line AC at right angle to AB equal in length to the diameter of the second given circle.\n<\/li>\n<li>Join BC.\n<\/li>\n<li>Bisect line BC so as to locate the centre P.\n<\/li>\n<li>With P as centre and radius PA or PB or PC, draw the required circle.\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ul>\n<li><strong><em>A Square of equal area to the sum of two given Squares.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and916.png\" alt=\"\"\/>Example 16: To draw a square equal in area to the sum of two given squares<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ol>\n<li>Draw a line AB equal in length to the side of one of the square.\n<\/li>\n<li>Draw another line AC perpendicular to AB and equal to the length of the side of the other square.\n<\/li>\n<li>Join BC. Then, construct a square on side BC. This is the required Square.\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ul>\n<li><strong><em>A Square of equal area to the difference of two given Squares.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and917.png\" alt=\"\"\/><strong>Example 17:<\/strong>  To draw a square equal in area to the difference of two given squares.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ul>\n<li>Draw a line AB equal to the length of side of the given smaller square.\n<\/li>\n<li>Erect a perpendicular at B.\n<\/li>\n<li>With A as centre and radius equal to the length of side of the given larger square, draw an arc to cut the perpendicular at point C.\n<\/li>\n<li>Construct a square on BC. This is the required square.\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ul>\n<li><strong><em>A square twice the area of a given square.<br \/>\n<\/em><\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and918.png\" alt=\"\"\/><strong>Example 18<\/strong>: To draw a square having Twice the area of a given square.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Method:<br \/>\n<\/strong><\/p>\n<ol>\n<li>Draw the given square ABCD.\n<\/li>\n<li>Draw the diagonal BD. This is the length of side of the required square.\n<\/li>\n<li>Construct the square BDEF. This is the required square.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Evaluation questions<br \/>\n<\/strong>1.  An irregular polygon is shown in the figure below.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and919.png\" alt=\"\"\/>\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0            AB = 70<br \/>\n            BC = 40<br \/>\n            DE = 75<br \/>\n            AE = 80<br \/>\n(a)  Construct<br \/>\n      (i)  the pentagon;<br \/>\n      (ii) a square equal in area to the given pentagon.<br \/>\n(b)  Draw and state the length of a diagonal of the square in (a)(ii) above.<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and920.png\" alt=\"\"\/>2.\u00a0\u00a0\u00a0\u00a0In the figure below, <strong>AD<\/strong> and <strong>BD<\/strong> are the diagonals of a pentagon<strong> ABCDE<\/strong>whose sides are <strong>BC = 40<\/strong>,<br \/>\nCD =35, DE =\u00a055 and &lt; DEA =90<sup>0<\/sup>.\u00a0(a)\u00a0 construct the pentagon<br \/>\n\u00a0   (b)\u00a0 state the length of side <strong>AE<\/strong> of the pentagon.<br \/>\n  (c)\u00a0 reduce the pentagon in (i) above to a triangle of equal area<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a03.  Construct a triangle ABC of sides AB = 50mm, AC = 60mm and BC = 55mm. Construct a<br \/>\nparallelogram equal in area with the triangle.<br \/>\n4.  Construct a square equal in area to a rectangle whose length and breadth are respectively 60mm and<br \/>\n 35mm.<br \/>\n5.  Three equilateral triangles have their sides 40mm, 55mm and 65mm respectively. Construct another<br \/>\n trianglewhose area is equal to the sum of the areas of these triangles. State the length of its sides.<\/p>\n<p>\u00a0<strong>Reading assignment<br \/>\n<\/strong>Technical drawing by JN Green. Pages 80-92.<br \/>\n<strong>Weekend Assignment<br \/>\n<\/strong><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and921.png\" alt=\"\"\/><strong>Objective<br \/>\n<\/strong><br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a01.  In the figure above, the area of rectangle JKLM is equal to A.  half the area of semi-circle JFE.  B.  the area of square KFGH.  C.  half the area of square KFGH.  D.  the area of semi-circle JFE.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and922.png\" alt=\"\"\/><em>         Use the figure below to answer questions <\/em>2 <em>and <\/em>3.<em><br \/>\n\t\t<\/em><br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a02.  What is the ratio of the areas of rectangle RSTU and square TVWX?  A.  1:1  B.  1:2  C.  1:3  D.  1:4.<br \/>\n3.  What is the value of angle &lt; SXY?  A.  450.  B.  600.  C.  750.  D.  900.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and923.png\" alt=\"\"\/>4.  Which two triangles have the same area in the figure below?<br \/>\n     A.  VTM and TUM.<br \/>\n     B.  TOM and MZU.<br \/>\n     C.  MUT and VST.<br \/>\n     D.  MOU and MVU.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a05.  Which of the following is equal in area to the polygon BCDEG shown below.  A.  CDG.  B.  CDGB.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and924.png\" alt=\"\"\/> C.  ABGEF.D.  AGF. <\/p>\n<p>\u00a0<br \/>\n\u00a0<strong>Theory<br \/>\n<\/strong><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and925.png\" alt=\"\"\/>1.  An irregular polygon is shown in the figure below.<br \/>\n     AB = 70<br \/>\n     BC = 40<br \/>\n     DE = 75<br \/>\n     AE = 80<\/p>\n<p>\u00a0(a)  Construct<br \/>\n      (i)  the pentagon;<br \/>\n      (ii) a square equal in area to the given pentagon.<br \/>\n(b)  Draw and state the length of a diagonal of the square in (a)(ii) above.<\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1132_Week8and926.png\" alt=\"\"\/>2.\u00a0\u00a0\u00a0\u00a0In the figure below, <strong>AD<\/strong> and <strong>BD<\/strong> are the diagonals of a pentagon<strong> ABCDE<\/strong>whose sides are <strong>BC = 40<\/strong>,<br \/>\nCD =35, DE =\u00a055 and &lt; DEA =90<sup>0<\/sup>.\u00a0(a)\u00a0 construct the pentagon<br \/>\n\u00a0   (b)\u00a0 state the length of side <strong>AE<\/strong> of the pentagon.<br \/>\n    (c)\u00a0 reduce the pentagon in (i) above to a triangle of equal area<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\t\t\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0 \u00a0WEEK EIGHT-NINE: DATE:\u2026\u2026\u2026\u2026\u2026\u2026 \u00a0 Topic: Equal area of planefigures Content: Examples on equivalent area&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,192],"tags":[],"class_list":["post-2253","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-technical-drawing"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2253","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2253"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2253\/revisions"}],"predecessor-version":[{"id":2254,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2253\/revisions\/2254"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}