Question

guys plz solve this

Answer 1

Answer:

Option(1)

Step-by-step explanation:

Given, s = d = 10 cm and Radius = 5 cm.

∴ Area of the shaded region = 4 * (Area of semicircle) - (Area of square)

= 4 * (πr²/2) - (s²)

= 2 * 3.14 * 25 - 10²

= 50 * 3.14 - 100

= 57 cm²

Hope it helps!

Answer 2

Each semicircle has same area as all have same diameter as side of the square.

In the square, there are 4 equal shaded portion 'looking like flower petals', and there are 4 equal unshaded portion also.

Method to find the area of the shaded region:

⇒ Area of a semicircle has to be found at first.

⇒ The area of a semicircle has to be doubled and then be subtracted from the area of the square, to get double of one such equal unshaded portion.

⇒ 2 times the area of double of one unshaded portion thus obtained has to be subtracted from the area of the square to get the answer.

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To find the double of area of one such semicircle, it is better to find the area of the circle formed by the same diameter of the semicircle.

→  Area of the square = 10² = 100  cm²

→  Diameter of the semicircle is 10 cm, thus the radius is 5 cm.

→  Area of the circle (Or area of twice the semicircle) = π(5)² = 25π  cm²

→  Difference of the areas of the circle and the square = 100 - 25π  cm²

→ Thus twice the area of one such unshaded portion = 100 - 25π  cm²

→  Double the area of twice one such unshaded portion = 2(100 - 25π)     = 200 - 50π  cm²

→  Area of the shaded region,

• Area of the square  -  Double the area of twice one such unshaded region.
• 100 - (200 - 50π)
• 100 - 200 + 50π
• 50π - 100
• 50 × 3.14 - 100
• 157 - 100
• 57  cm²

Hence the area of the shaded region is 57  cm².

Thus the answer is option 1.