Answer: 78 units²
Step-by-step 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.
[tex]A_{\triangle}=\dfrac{base\times height}{2}=\dfrac{9\times 12}{2}=54\\\\A_{\square}=length \times width = 12 \times 2 =24\\\\A_{trapezoid}=A_{\triangle}+A_{\square}=54+24=\large\boxed{78}[/tex]
You can also use the trapezoid rule:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h\\\\\\.\quad = \dfrac{(9+2)+(2)}{2}\cdot 12\\\\\\.\quad = \dfrac{13}{2}\cdot 12\\\\\\.\quad =13\cdot 6\\\\\\.\quad = \large\boxed{78}[/tex]
