Question

What is the area of the trapezoid shown below?

Answer 1

Answer: 78 units²

Explanation:

Use Pythagorean Theorem to find the base of the triangle:

x² + 12² = 15²

x² + 144 = 225

x² = 81

x = 9

Now, separate the figure into two shapes --> triangle and rectangle.

`A_(\triangle)=(base* height)/(2)=(9* 12)/(2)=54\\\\A_(\square)=length * width = 12 * 2 =24\\\\A_(trapezoid)=A_(\triangle)+A_(\square)=54+24=\large\boxed{78}`

You can also use the trapezoid rule:

`A=(b_1+b_2)/(2)\cdot h\\\\\\.\quad = ((9+2)+(2))/(2)\cdot 12\\\\\\.\quad = (13)/(2)\cdot 12\\\\\\.\quad =13\cdot 6\\\\\\.\quad = \large\boxed{78}`