Answer to Question #158221 in Geometry for Janine Leodones

Question

The bases of an isosceles trapezoid are 12 inches and 18 inches, and the legs are 5

inches. A rectangle equal in area to the trapezoid has one dimension 6 inches.

Find the other dimension.

Answer 1

Find the height of the isosceles trapezoid $h$ from the Pythagorean Theorem

$$5^2=h^2+(\dfrac{18-12}{2})^2$$

Then $h=4\ in$

The area of the trapezoid

$$A_t=(\dfrac{18+12}{2})h=15(4)=60\ {in}^2$$

The area of the rectangle

$$A_r=length\times width=6\times width$$

Given $A_t=A_r$

$$6\times width=60$$

$$width=10\ in$$

A rectangle is equal in area to the trapezoid has another dimension of 10 inches.