Area of a composite figure
The figure consists of a rectangle and a semicircle.
The diameter of the semicircle is the width of the rectangle.
The area of a rectangle of length L and width W is:
[tex]A_r=W\cdot L[/tex]
The given measures are W = 8 and L = 13, thus:
[tex]\begin{gathered} A_r=8\cdot13 \\ A_r=104 \end{gathered}[/tex]
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]
The area of a semicircle (half a circle) is:
[tex]A_{sc}=\frac{\pi r^2}{2}[/tex]
As mentioned above, the diameter of the semicircle equals the width of the rectangle, thus d = 8
The radius is half the diameter, thus: r = 4. Substituting:
[tex]\begin{gathered} A_{sc}=\frac{\pi\cdot4^2}{2} \\ \text{Calculating:} \\ A_{sc}=8\pi \\ A_{sc}\approx25.1 \end{gathered}[/tex]
The total area is:
A = 104 + 25.1
A = 129.1
