Question

The area of a trapezoid is 87m^2, the base is 13m long, and the height is 4m. Find the length of the top of the trapezoid.

Answer 1

The formula of an area of a trapezoid:

$A=\dfrac{base_1+base_2}{2}\cdot height$

We have:

$A=87\ m^2\\\\base_1=13\ m\\\\height=4\ m$

Substitute:

$\dfrac{13+base_2}{2}\cdot4=87\\\\(13+base_2)\cdot2=87\qquad|\text{use distributive property}\\\\(13)(2)+(base_2)(2)=87\\\\26+2base_2=87\qquad|\text{subtract 26 from both sides}\\\\2base_2=61\qquad|\text{divide both sides by 2}\\\\base_2=30.5\ m$

Answer: 30.5 m