{"id":19776,"date":"2018-02-01T11:20:25","date_gmt":"2018-02-01T11:20:25","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=19776"},"modified":"2020-11-26T15:09:40","modified_gmt":"2020-11-26T09:39:40","slug":"math-labs-activity-derive-formula-finding-area-parallelogram","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/math-labs-activity-derive-formula-finding-area-parallelogram\/","title":{"rendered":"Math Labs with Activity – Derive a Formula for Finding the Area of a Parallelogram"},"content":{"rendered":"
OBJECTIVE<\/strong><\/span><\/p>\n To derive a formula for finding the area of a parallelogram.<\/p>\n Materials Required<\/strong><\/span><\/p>\n Theory<\/strong><\/span> Procedure<\/strong> <\/span> Observations and Calculations<\/strong><\/span> Result<\/strong> <\/span> Remarks:<\/strong> The teacher must discuss the case where the perpendicular falls outside the base as shown in Figure 26.4. Math Labs with Activity<\/a>Math Labs<\/a>Math Lab Manual<\/a>Science Labs<\/a>Science Practical Skills<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Math Labs with Activity – Derive a Formula for Finding the Area of a Parallelogram OBJECTIVE To derive a formula for finding the area of a parallelogram. Materials Required Two sheets of white paper A sheet of glazed paper A geometry box A tube of glue A pair of scissors Theory It has been geometrically … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[],"yoast_head":"\n\n
\nIt has been geometrically proved that the area of a parallelogram having base =b units and height =h units is given by area =(b x h) square units.<\/p>\n
\nStep 1:<\/strong> Construct a parallelogram ABCD having base=b units and height =h units on a sheet of white paper as shown in Figure 26.1.
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\nStep 2:<\/strong> Make an exact copy of the parallelogram ABCD on the glazed paper. Fold the glazed paper along the line that passes through the point D and cuts the side AB such that the part of the line AB that\u00a0lies on one side of the line of fold falls on the other part. Make a crease and unfold the paper. Draw a line X1<\/sub>Y1<\/sub> along the line of fold. Mark the point E where X1<\/sub>Y1<\/sub> cuts the side AB as shown in Figure 26.2.
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\nStep 3:<\/strong> Cut the \u0394AED and the quadrilateral EBCD. Label the triangle as \u0394A’E’D’. Paste the quadrilateral EBCD and the\u00a0 \u0394A’E’D’ on a new sheet of white paper as shown in Figure 26.3.
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\nStep 4:<\/strong> Record your observations.<\/p>\n
\nWe observe that a rectangle is formed when the two parts of the parallelogram are arranged as shown in Figure 26.3.
\nLength of the rectangle DCE’E =DC =b units (from Figure 24.1). Breadth of the rectangle DCE’E=ED = h units.
\narea of the rectangle DCE’E = (b x h) square units.
\nHence, the area of the parallelogram ABCD = (b x h) square units.<\/p>\n
\nThe area of a parallelogram is equal to the product of its base and height.<\/p>\n
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\nABCD is a parallelogram in which the perpendicular from the point A falls outside the base DC. In such a case we drop a perpendicular AG from the point A on the side DC (produced) and another perpendicular CH from the point C on the side AB (produced). Mark the points E and F where the perpendiculars AG and CH intersect the sides BC and AD respectively. Cut\u00a0 \u0394DEC and place it over \u0394CEG. Also, cut \u0394ABE and place it over \u0394HAF. We thus get a rectangle HAGC whose area is given by area =AB x AG.
\nSo, area of the given parallelogram = AB x AG =base x height.<\/p>\n