Question

A trapezoid has an area of 20 cm2 and a height z cm. The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm. Find the height, z, of the trapezoid. In your final answer, include all of the formulas and calculations necessary.

Answer 1

Area of a trapezoid = ½(a + b)h, where a and b are the lengths of the parallel sides and h is its height. 

From your information 20 = ½(2z + 3 + 6z – 1)z = ½(8z + 2)z = z(4z + 1) 

Solve 20 = 4z² + z which is 0 = 4z² + z – 20 using the quadratic formula