Question

1. calculate the area of each shape. show all your work and label your answers! a) a = 1/2bh b) a = 1/2(b1 + b2)

Explanation:

Step1: Identify base and height for triangle

For the triangle in part a), base $b = 9$ and height $h=12$.

Step2: Calculate area of triangle

Using the formula $A=\frac{1}{2}bh$, we substitute $b = 9$ and $h = 12$. So $A=\frac{1}{2}\times9\times12=\frac{1}{2}\times108 = 54$.

Step3: Identify bases and height for trapezoid

For the trapezoid in part b), $b_1=9$, $b_2=9 + 4+4=17$, and $h = 17$.

Step4: Calculate area of trapezoid

Using the formula $A=\frac{1}{2}(b_1 + b_2)h$, we substitute $b_1 = 9$, $b_2=17$ and $h = 17$. Then $A=\frac{1}{2}(9 + 17)\times17=\frac{1}{2}\times26\times17=13\times17 = 221$.

Answer:

a) The area of the triangle is 54.
b) The area of the trapezoid is 221.