To solve for the area of this composite shape, we have to solve for the area of the trapezoid and the area of the half-circle then, add it.
The area of the trapezoid can be solved using the formula below:
[tex]A=\frac{b_1+b_2}{2}\times h[/tex]Our bases here are 8 and 20, while the height is 8 inches.
[tex]\begin{gathered} A=\frac{8+20}{2}\times8 \\ A=\frac{28}{2}\times8 \\ A=14\times8 \\ A=112in^2 \end{gathered}[/tex]The area of the trapezoid is 112 square inches.
This time, let's solve for the area of the semicircle. The formula for this would be half the area of the full circle. Based on the figure, the radius is 4 inches.
[tex]\begin{gathered} A=\frac{\pi r^2}{2} \\ A=\frac{3.14(4^2)}{2} \\ A=\frac{(3.14)(16)}{2} \\ A=\frac{50.24}{2} \\ A=25.12in^2 \end{gathered}[/tex]The area of the circle is 25.12 square inches.
Therefore, the total area of the composite shape is 112 + 25.12 = 137.12 square inches.
This time, we are now going to solve for the perimeter. Perimeter is the total length of the outside part of each shape. In this case, we are going to solve for the circumference of the semicircle and also, the perimeter of the trapezoid excluding the shorter base since it's inside the shape already, not outside.
To solve for the circumference of the semicircle, we have:
[tex]\begin{gathered} C=\frac{2\pi r}{2} \\ C=\pi r \\ C=3.14\times4 \\ C=12.56inches \end{gathered}[/tex]The perimeter of the trapezoid is:
[tex]\begin{gathered} P=b_2+leg_1+leg_2 \\ P=20+10+10 \\ P=40\text{inches} \end{gathered}[/tex]Therefore, the total perimeter of the composite shape is 12.56 + 40 = 52.56 inches.
To summarize:
Perimeter = 52.56 inches
Area = 137.12 square inches
