Question

Find the area of the shaded region below. Give your answer in terms of T. 12m 5m

Answer 1

The area of the shaded region is [(169π/4)-60]m².

• The length of the rectangle is 12 m.
• The breadth of the rectangle is 5 m.
• The area of the rectangle = length * breadth.
• The area of the rectangle = 12 * 5
• The area of the rectangle = 60m²
• Let h be the diagonal of the rectangle.
• Using the Pythagorean theorem,
• h² = 12² + 5²
• h² = 144 + 25
• h² = 169
• h = √169
• h = 13
• The diagonal of the rectangle is also the diameter of the circle.
• Let r be the radius of the circle.
• 2r = 13
• r = 13/2m
• The area of the circle is πr².
• The area of the circle = π(13/2)²
• The area of the circle = (169π/4)m²
• The area of the shaded region equals the area of the circle minus the area of the rectangle.
• The area of the shaded region = [(169π/4) - 60]m²

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