Question

Find the area of the shaded region. Use 3.14 to represent pi. Hint: You need to find height of triangle.A: 329.04B: 164.52C: 221.04D: 272.52

Answer 1

The area of the shaded region is 164.52 inches squared

Here, we wan to calculate the area of the shape given

From what we have, there is a triangle and a semi-circle

So the area of the shape is the sum of the areas of the triangle and the semi-circle

Mathematically, we can have this as;

`\begin{gathered} \text{Area of triangle = }(1)/(2)\text{ }*\text{ b }*\text{ h} \\ \\ \text{Area of semicircle = }\frac{\pi\text{ }* r^2}{2} \end{gathered}`

where b represents the base of the triangle which is the diameter of the semicircle

The radius of the semicircle is 6 inches and the diameter is 2 times of this which equals 2 * 6 = 12 inches

The height of the triangle is 18 inches

The radius of the semicircle is 6 inches as above

Thus, we have the area of the shape as follows;

`\begin{gathered} ((1)/(2)*\text{ 18 }*\text{ 12) + (}\frac{3.14\text{ }*6^2}{2}) \\ \\ =\text{ 108 + 56.52} \\ \\ =\text{ 164.52 inches squared} \end{gathered}`