To find the area of the shaded region you divide the figure into:
2 semicircles and one triangle, as fllow:
First semicircle and triangle:
Second semicircle:
The area of the shaded area is the sum of Area 1 and 2 (semicircle and triangle) less the area of semicircle 3.
[tex]A_S=A_1+A_2-A_3[/tex]Area 1:
The area of a semicircle is:
[tex]A=\frac{\pi\cdot r^2}{2}[/tex]
The semicirlce 1 has a diameter of (4cm+4cm+8cm=16cm) the radius is the half of the diameter (8cm):
[tex]A_1=\frac{\pi\cdot(8\operatorname{cm})^2}{2}=\frac{\pi64cm^2}{2}=32\pi cm^2[/tex]Area 2:
The area of a triangle is:
[tex]A=\frac{1}{2}b\cdot h[/tex]
The given triangle has height of 3cm and a base of 8cm:
[tex]A_2=\frac{1}{2}(8\operatorname{cm})(3\operatorname{cm})=\frac{24cm^2}{2}=12cm^2[/tex]
Area 3:
The semicirlce has a diameter of 8cm, the radios os the hal od the diameter (4cm):
[tex]A_3=\frac{\pi\cdot(4\operatorname{cm})^2}{2}=\frac{\pi16cm^2}{2}=8\pi cm^2[/tex]
Then, the area of the shaded region is approximately: 87.40 squared centimeters[tex]\begin{gathered} A_S=32\pi cm^2+12cm^2-8\pi cm^2 \\ \\ A_S=24\pi cm^2+12cm^2 \\ \\ A_S\approx87.40cm^2 \end{gathered}[/tex]
