Question

If the area of a trapezoid is 46 sq. cm. and its height is 4 cm. Find the shorter base if itslonger base is 15 cm.

Answer 1

We are given the following information about a trapezoid.

Area = 46 sq cm

Height = 4 cm

Longer base = 15 cm

We are asked to find the shorter base of the trapezoid.

Recall that the area of a trapezoid is given by

$A=\frac{a+b}{2}\cdot h$

Let us substitute the given values and solve for the shorter side of the trapezoid.

$\begin{gathered} 46=(\frac{a+15}{2})\cdot4 \\ 2\cdot46=(a+15)\cdot4 \\ 92=(a+15)\cdot4 \\ \frac{92}{4}=a+15 \\ 23=a+15 \\ a=23-15 \\ a=8\; cm \end{gathered}$

Therefore, the shorter base of the trapezoid is 8 cm