Question

1. calculate the area of each shape. show your work and label your answers. a) $a=\frac{1}{2}cdot bcdot h$ b) $a = \frac{1}{2}cdot(b_1 + b_2)cdot h$

Explanation:

Step1: Identify values for triangle

For the triangle, the base $b = 15$ and the height $h = 29$.

Step2: Calculate triangle area

Using the formula $A=\frac{1}{2}\cdot b\cdot h$, we substitute the values: $A=\frac{1}{2}\times15\times29=\frac{435}{2} = 217.5$.

Step3: Identify values for trapezoid

For the trapezoid, $b_1=10$, $b_2 = 5 + 10+ 5=20$, and $h = 18$.

Step4: Calculate trapezoid area

Using the formula $A=\frac{1}{2}\cdot(b_1 + b_2)\cdot h$, we substitute the values: $A=\frac{1}{2}\times(10 + 20)\times18=\frac{1}{2}\times30\times18=270$.

Answer:

a) The area of the triangle is $217.5$.
b) The area of the trapezoid is $270$.