5. In a trapezium ABCD, AB | | DC, AB = 30 cm, BC15 cm, DC 44 cm and A

1.	5. In a trapezium ABCD, AB \| \| DC, AB = 30 cm, BC15 cm, DC 44 cm and AD 13 cm. Find thearea of the trapezium.
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 cmBC = 15 cmCE = 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 = area14h/2 = 84h = 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

5. In a trapezium ABCD, AB | | DC, AB = 30 cm, BC15 cm, DC 44 cm and AD 13 cm. Find thearea of the trapezium.

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 cmBC = 15 cmCE = 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 = area14h/2 = 84h = 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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