Question

Find the area of polygon ABCDEFG. The measurements (in cm) are shown in the figure.​

Answer 1

SOLUTION :-

=>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.