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 \(A = \pi r^{2}\). Given \(r = 5\mathrm{cm}\), so \(A_{circle}=\pi\times5^{2}=25\pi\mathrm{cm}^{2}\).

Step2: Calculate the area of the two right - angled triangles

The formula for the area of a right - angled triangle is \(A=\frac{1}{2}bh\). For each triangle, \(b = 6\mathrm{cm}\) and \(h = 4\mathrm{cm}\). The area of one triangle is \(\frac{1}{2}\times6\times4 = 12\mathrm{cm}^{2}\). The area of two triangles is \(2\times12=24\mathrm{cm}^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{circle}-A_{triangles}\). So \(A=(25\pi - 24)\mathrm{cm}^{2}\).

Answer:

\((25\pi - 24)\mathrm{cm}^{2}\) (the third option)