Question

The area of an isosoles trapezoid is 45cm squared, and it's height is 5cm. Find the perimeter if the length of a leg is 2/3 of the sum of the bases.

Answer 1

Perimeter = 42 cm.

Explanation:

The 2 legs are equal in length as it is an isosceles trapezoid.

Area of trapezoid = (h/2)(a + b) where a and b are the parallel bases.

So

(5/2) (a + b) = 45

a + b = 45 * 2/5 = 18 cm.

We are given that the length of a leg (L) is 2/3 * sum of the bases, so:

L = 2/3(a + b)

= 2/3 * 18

= 12 cm.

The perimeter = a + b + 2L

= 18 * 2*12

= 42 cm.