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

Answer: 2.11cm

Explanation:

Given the following :

The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm

The area of trapezoid is calculated using the formula:

1/2(a + b) × h

Where ;

a = Length of side 1

b = length of side 2

h = height

Take a = (2z + 3) and b = (6z – 1), h = z

Therefore ;

1/2 (2z + 3 + 6z - 1) × z

Opening the bracket

(z + 1.5 + 3z - 0.5) × z

(4z + 1 ) × z = 20cm^2

4z^2 + z = 20cm^2

Using Quadratic formula:

4z^2 + z - 20 = 0

a = 4, b = 1, c = - 20

(-b±√b^2 -4ac) / 2a

Z = 2.11 or - 2.364

z cannot be negative, therefore,

Z = 2.11 cm