Question

in the given figure O is the centre of the circle aob is the diameter AC is equal to 12 cm and BC equal to 16 cm find the area of shaded region​

Answer 1

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Answer 2

Area of shaded region​ = 29.07 cm.

Given:

• AC is equal to 12 cm.
• BC equal to 16 cm.

To find:

       Area of shaded region​.

Formula used:

• Area of semicircle = $\frac{\pi }{8}$ × (Diameter)²
• Pythagoras theorem.   AB² = AC² + BC²
• Area of triangle = $\frac{1}{2}$ × base ×height

Explanation:

• From property of circle ∠ACB =90°
• From Pythagoras theorem,

             AB² = AC² + BC²

             AB² = 12²+16²

             AB² = 144 + 256

             AB² = 400

             AB = 20 cm.

• AB is diameter of circle

• Area of semicircle = $\frac{\pi }{8}$ × (Diameter)²

                                      = $\frac{\pi }{8}$ × (AB)²

                                      = $\frac{\pi }{8}$ × (20)²

                                      = 157.07 cm².

• Area of ΔABC= $\frac{1}{2}$ × BC ×AC

                                = $\frac{1}{2}$ × 16 × 12

                                = 128 cm²

• Area of shaded region​ = Area of semicircle - Area of triangle
• Area of shaded region​ = 157.07 - 128

                                               = 29.07 cm.

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