Answer:
212.52 cm²
Explanation:
You are going to use three different area formulas to solve this, adding them together to get your total area.
The area of a circle is πr² so to find the area of a half-circle we will, well, take half of it: πr² / 2. The diameter is given as 12 cm. The radius (r) is half of the diameter, so this measurement is 6 cm. Using 3.14 as our approximation for pi, the area of the half-circle is 3.14(6)² / 2 = 3.14(36) / 2 = 113.04 / 2 = 56.52 cm²
The area of a rectangle is length multiplied by width. Assuming the the widths of these rectangles are equidistant, the widths will be the same as our radius in the previous section. We are given the lengths making this a simple calculation. The area is 8(6) = 48 cm². There are two rectangles so we multiply this by 2 and the result is 96 cm²
The area of a triangle can be found using (1/2) base x height, or (base x height) / 2. This will help with those two triangles at the bottom of the diagram. The base is the same as the width of the rectangles and the radius of the half-circle so we can use that same 6 cm measurement here. The area is 6(10) / 2 = 60 / 2 = 30 cm². There are two triangles to we multiply this by 2 and get 60 cm²
Add them all together now and don't forget those units! 56.52 + 96 + 60 = 212.52 cm²