Question

2-18 determine the area of each of the following figures. assume that all angles that look like right angles are right angles. area of △ = $\frac{1}{2}bcdot h$ area of □ = bcdot h

Explanation:

Step1: Identify the shapes

The figure is composed of a trapezoid on top of a rectangle.

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is $A_{t}=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, $a = 4$, $b=8$, and $h = 3$. So $A_{t}=\frac{(4 + 8)\times3}{2}=\frac{12\times3}{2}=18$ square feet.

Step3: Calculate the area of the rectangle

The formula for the area of a rectangle is $A_{r}=l\times w$. Here, $l = 8$ and $w = 2$, so $A_{r}=8\times2 = 16$ square feet.

Step4: Calculate the total area

The total area $A=A_{t}+A_{r}=18 + 16=34$ square feet.

Answer:

34 square feet