a field in the shape of trapezium has its parallel sides as 16 m and 12m while the non parallel sides are 13m and 15m find the area of the field
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Consider a trapezium ABCD with AB=20 m, BC = 6 m, CD = 30 m and DA = 8 m.
Drop a perpendicular from A on CD to meet that line at E. We consider the figure ABCD as a combination of a rectangle ABCE and a triangle AED. <B = <C = 90.
Area of ABCE = 20*6 = 120 sq m.
Area of AED can EB found by Heron’s formula where 2s =6+10+8 = 24, or s = 12
Area AED = [12(12–6)(12–10)(12–8)]^0.5
= [12*6*2*4]^0.5
= 24 sq m.
Total area of ABCE + AED = 120+24 = 144 sq m.
Drop a perpendicular from A on CD to meet that line at E. We consider the figure ABCD as a combination of a rectangle ABCE and a triangle AED. <B = <C = 90.
Area of ABCE = 20*6 = 120 sq m.
Area of AED can EB found by Heron’s formula where 2s =6+10+8 = 24, or s = 12
Area AED = [12(12–6)(12–10)(12–8)]^0.5
= [12*6*2*4]^0.5
= 24 sq m.
Total area of ABCE + AED = 120+24 = 144 sq m.
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