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

Height z= 2.115 cm

Explanation:

The formula for area of a trapezoid is ;

A=1/2(a+b)h where A is area, a and b are the lengths of parallel sides and h is the height of the trapezoid.

Given in the question;

A= 20 cm²

a=( 2z + 3 ) cm

b= (6z-1) cm

h= z =? unknown

Substitute in the formula as;

A=1/2(a+b)h

20=1/2(2z+3+6z-1)z -----------multiply both sides of the equation by 2

40= (2z+3+6z-1)z  -----------collect like terms as

40 =(2z+6z+3-1)z

40=(8z+2)z -----open brackets as

40=8z²+2z --------- form a quadratic equation

8z²+2z-40 = 0 -----solve the quadratic equation to find value of z

z²+0.25z-5=0

z= 2.115