Answer:
Exact Area of shaded region = 141.39cm²
Step-by-step explanation:
Quadrant of a circle - Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. When it comes to circle, the quarter of a circle is called a quadrant, which is a sector of 90°.
area of circle =πr²
area of quadrant of a circle = πr²/4
where r is the radius of the circle.
In the given figure there are 2 types of quadrants of circle are present
one with radius AB (bigger )
another with radius AB/2 (smaller)
Now area of quadrant having radius = AB
⇒ π(AB) ²/4
here AB is the side of square
so AB = 12cm
substituting this in the area of quadrant formula
area of bigger quadrant = π(12²)/4
area₁ = 144×π/4
area₁ = 144×3.142/4
area₁ = 113.112cm²
now area of smaller quadrant = π(AB/2) ²/4
area ₂ = π(6) ²/4
area ₂ = 36π/4
area ₂ = 9×π
area ₂ = 28.278cm²
Now it is clear from the given figure,
area of shaded region is = area₁ - area₂ +2×area₂
= 113.112cm² - 28.278cm² + 2× 28.278cm²
= 113.112cm² + 28.278cm²
= 141.39cm² (answer)
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