Question

a composite figure is shown. the figure has been decomposed along the dotted line.
find the area of each of the parts. then find the combined area.
triangle area: \\(\square\\) feet\\(^2\\)
trapezoid area: \\(\square\\) feet\\(^2\\)
combined area: \\(\square\\) feet\\(^2\\)

Explanation:

Step1: Calculate Triangle Area

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. The base of the triangle is 8 ft and the height is 2 ft. So, $A_{triangle} = \frac{1}{2} \times 8 \times 2 = 8$ square feet.

Step2: Calculate Trapezoid Area

The formula for the area of a trapezoid is $A = \frac{1}{2} \times (a + b) \times h$, where $a$ and $b$ are the lengths of the two parallel sides, and $h$ is the height. Here, $a = 8$ ft, $b = 4$ ft, and $h = 4$ ft. So, $A_{trapezoid} = \frac{1}{2} \times (8 + 4) \times 4 = \frac{1}{2} \times 12 \times 4 = 24$ square feet.

Step3: Calculate Combined Area

To find the combined area, we add the area of the triangle and the area of the trapezoid. So, $A_{combined} = 8 + 24 = 32$ square feet.

Answer:

Triangle area: $\boldsymbol{8}$ feet²
Trapezoid area: $\boldsymbol{24}$ feet²
Combined area: $\boldsymbol{32}$ feet²