Question

A triangle is placed in a semicircle with a radius of 8 cm as shown below

Answer 1

To find the area of the shaded region:

1. Find the area of the semicircle:

`\begin{gathered} A=(\pi *r^2)/(2) \\ \\ A=\frac{3.14*(8cm)\placeholder{⬚}^2}{2}=(3.14*64cm^2)/(2)=100.48cm^2 \end{gathered}`

2. Find the area of the triangle:

the base of the triangle is the diameter of the semicircle (twice the radius)

`\begin{gathered} A=(1)/(2)b*h \\ \\ A=(1)/(2)(16cm)(8cm)=(128)/(2)cm^2=64cm^2 \end{gathered}`

3. Subtract the area of the triangle from the area of the semicirle:

`A_(shaded)=100.48cm^2-64cm^2=36.48cm^2`Then, the area of the shaded region is 36.48 square centimeters