Question

what is the area of the shaded region?
(25π − 48) cm²
(25π − 30) cm²
(25π − 24) cm²
(25π − 12) cm²

Explanation:

Step1: Calculate the area of the circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r = 5\) cm.

$$A_{circle}=\pi\times5^{2}=25\pi\space cm^{2}$$

Step2: Calculate the area of the two non - shaded triangles

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). For each triangle, \(b = 6\) cm and \(h = 4\) cm.
The area of one triangle: \(A_{triangle1}=\frac{1}{2}\times6\times4 = 12\space cm^{2}\)
The area of two triangles: \(A_{two - triangles}=2\times\frac{1}{2}\times6\times4=24\space cm^{2}\)

Step3: Calculate the area of the shaded region

The area of the shaded region \(A_{shaded}=A_{circle}-A_{two - triangles}\)

Answer:

\((25\pi - 24)\space cm^{2}\)