Question

32. In the figure, ABCD is a square of side 14 cm and ABCEA and DAFCD are quarters of circle
of radius 14 cm. Find the area of the shaded region,​

Answer 1

Solution :-

As we know that,

• All angles of square are equal to 90° .
• so, area of quadrant of a square = (90/360)πr² = (1/4)πr² .
• Area of a right angled ∆ = (1/2) * Base * height .
• Area of half leaf = Area of quadrant - Area of a right angled ∆ .

so,

→ Area of half leaf = Area of quadrant - Area of a right angled ∆ = (1/4)π(a)² - (1/2)a² = (1/2)a²[π / 2 - 1]

then,

→ Area of 1 leaf = 2 * (1/2)a²[π / 2 - 1]

given that,

• a = 14 cm.

therefore,

→ Area of shaded region = 14²[π/2 - 1] = 196(22/14 - 1) = 196(22 - 14)/14 = 14 * 8 = 112 cm². (Ans.)

Hence, Area of shaded region will be 112 cm².

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