Step 1: Problem
Step 2: Concept
The area of the figure is the sum of the area of a triangle and a semi-circle.
Step 3: Method
Perimeters
Height of the triangle = 15cm
Base of the triangle = 2 x Radius of the semi-circle = 2 x 8 = 16cm
Radius r = 8cm
[tex]\begin{gathered} \text{Area of the triangle = }\frac{Base\text{ x Height }}{2} \\ \\ =\text{ }\frac{16\text{ x 15}}{2} \\ =\text{ }\frac{240}{2} \\ =120cm^2 \\ \text{Area of the semi-circle = }\pi r^2 \\ \pi\text{ = 3.14} \\ =\text{ 3.14 }\times8^2 \\ =\text{ 3.14 x 64} \\ =200.96cm^2 \end{gathered}[/tex]Step 4: Final answer
Area of the figure = Area of triangle + Area of semi-circle
= 120 + 200.96
= 320.96
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