Question

what is the area of the shaded region? (25π - 48) cm² (25π - 30) cm² (25π - 24) cm² (25π - 12) cm² 6 cm 1 cm 5 cm 6 cm 1 cm

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

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

The base of each right - angled triangle is $6$ cm and the height is $4$ cm. The formula for the area of a triangle is $A=\frac{1}{2}bh$.
The area of one triangle is $\frac{1}{2}\times6\times4 = 12$ $cm^{2}$.
The area of two such triangles is $2\times12=24$ $cm^{2}$.

Step3: Calculate the area of the shaded region

The area of the shaded region is the area of the circle minus the area of the two triangles. So $A = 25\pi- 24$ $cm^{2}$.

Answer:

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