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The area of the shaded region is .
Solution:
Given radius = 4 cm
Diameter = 2 × 4 = 8 cm
Let us first find the area of the semi-circle.
Area of the semi-circle =
Area of the semi-circle = cm²
Angle in a semi-circle is always 90º.
∠C = 90°
So, ABC is a right angled triangle.
Using Pythagoras theorem, we can find base of the triangle.
cm
Base of the triangle ABC = cm
Height of the triangle = 4 cm
Area of the triangle ABC =
Area of the triangle ABC = cm²
Area of the shaded region
= Area of the semi-circle – Area of the triangle ABC
=
=
Hence the area of the shaded region is .