InterviewSolution
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InterviewSolution
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5. In a trapezium ABCD, AB | | DC, AB30 cm, BQ13 cm. Find the- 15 cm, DC 44 cm and ADarea of the trapezium. |
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Answer» Translate D by vector AB, and let its image be E. Quadrilateral ABED is a parallelogram, so EB is equal in length to DA. Now consider triangle EBC. All three sides are known. EB = 13 cm BC = 15 cm CE = 14 cm Use Heron's formula. For triangles that is. There is no Heron's formula for quadrilaterals. (13 + 15 + 14)/2 = 21 area(EBC) = √[21(21 - 13)(21 - 15)(21 - 14)] = √[21(8)(6)(7)] = √(7056) = 84 Let EC be the base of that triangle. Find its corresponding height. (base)(height)/2 = area 14h/2 = 84 h = 12 The height of triangle EBC is 12 cm. That is also the height of the trapezium. area(ABCD) = (AB + DC)h/2 = (30 + 44)(12)/2 = 444 cm² |
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