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Find the area of polygon ABCDEFG. The measurements (in cm) are shown in the figure. |
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Answer» N :- =>The polygon can be SPLIT into two trapeziums and a TRIANGLE.=>So, the area of polygon ABCDEFG is given by the sum of the area of trapezium ABCG and CDFG and the area of triangle DEF.=>Height of trapezium ABCG = 3 cm=>Height of trapezium CDFG = (6 – 3) = 3 cm=>Height of triangle DEF = (8 – 6) = 2 cm=>Area of trapezium ABCG = (sum of parallel sides) × height/2 = (4 + 7)×3/2 = 33/2 = 16.5 cm²=>Area of trapezium CDFG = (7 + 4) ×3/2 = 33/2 = 16.5 cm²=>Area of triangle DEF = (base ×height)/2 = (4 × 2)/2 = 8/2 = 4 cm²=>So, area of polygon ABCDEFG = area of ABCG + area of CDFG + area of DEF=> 16.5 + 16.5 + 4 = 37 cm².Therefore, the area of polygon ABCDEFG is 37cm². |
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