Question

All the sides of a isosceles trapezium touch a circle. The lengths of parallel sides of the trapezium are 4 & 9. Find the area of the trapezium

Answer 1

Answer:

An isosceles trapezium, ABCD, is circumscribed about a circle of radius 2 cm and the area of the trapezium is 40 cm sq. What will be the equal sides of the trapezium?

The distance between the parallel sides, AB and CD = 4 cm, same as the diameter of the circle.

Area of the trapezium, ABCD = 40 sq cm.

The combined length of the parallel sides, AB+CD = 40*2/4 = 20 cm.

If one parallel side, AB = 4 cm. the other parallel side, CD = 16 cm.

(CD-AB)/2 = (16–4)/2 = 6

The equal sides BC = DA = [6^2+4^2]^0.5 = [36+16]^0.5 = 52^0.5 = 7.211102551 cm.

Step-by-step explanation: