### Home > CCG > Chapter 6 > Lesson 6.2.3 > Problem6-76

6-76.

Find the area and perimeter of the trapezoid at right.

Separate the trapezoid into $3$ separate figures, a right triangles at left, a rectangle in the middle, and a right triangle at right.

Label the leg between the parallel bases as, $h$, for both triangles. Label the second leg on the right triangle at right, $a$ and on the left triangle, $d$. Solve for $a$, $d$, and $h$.

$\sin(65º)=\frac{h}{8}$ and $\cos(65º)=\frac{a}{8}$

Label the hypotenuse on the right triangle at right, $e$. Solve for $d$ and $e$.

$\sin(72º)=\frac{h}{e}$ and $\cos(65º)=\frac{d}{e}$

Area $\approx100.55$ yds$^2$
Perimeter $\approx43.36$ yds