Question

the lengths of two parallel sides of a Trapezium are 91 cm and 51 cm and the lengths of two other sides are 37 cm and 13 cm respectively determine the area of trapezium​

Answer 1

Answer:

The length of two parallel sides of a trapezium are 91 cm and 51 cm, and the length of the two other sides are 37 cm and 13 cm respectively. What is the area of the Trapezium?

From the two different top corners of the trapezium, lower the two heights to the 91cm side. Get 2 right triangles with the same one leg (H). One triangle has a second leg (a) and a hypotenuse of 37cm. The second triangle has a second leg (b) and a hypotenuse of 13cm.

a+b = 91–51 => b = 40 - a

Same leg (height):

37^2 - a^2 = 13^2 - (40-a)^2

1369 - a^2 = 169 - 1600 +80a - a^2

80a = 2800

a = 35

H^2 = 37^2 - 35^2 = 144

H = 12cm

A = (51+91)/2 * H = 142*12/2 = 852 cm^2