Question

find the area of shaded region(step by step)​

Answer 1

Given:

✰ Diameter of a circle = 16 cm

✰ Diagonal of a square = 16 cm

To find:

✠ The area of shaded region

Solution:

✵ First we will find out the radius of the circle to find the area of a circle by using formula. After that we will find out the area of a square then, we will substract the area of a square from the area of a circle to find the area of shaded region.

⤀Radius = Diameter/2

⤀Radius = D/2

⤀Radius = 16/2

⤀Radius = 8 cm

Area of a circle = πr²

Put the values in,

• Area of a circle = 3.14 × 8²

• Area of a circle = 3.14 × 8 × 8

• Area of a circle = 25.12 × 8

• Area of a circle = 200.96

• Area of a circle = 200.1 cm²

✵ Now, let's find out the area of a square. For that we must have side of a square. When you have a look at the attachment you can clearly see that the diameter of a circle is equal to diagonal of a square which is 16 cm So, we can easily calculate the side by using the formula of diagonal of square.

Diagonal of a square = side√2

• 16 = side√2

• side = 16/√2

Now, rationalize

• side = (16 × √2)/(√2 ×√2)

• side = 16√2/(√2)²

• side = 16√2/2

• side = 8√2

Now,

Area of a square = side × side

• Area of a square = ( side )²

• Area of a square = ( 8√2 )²

• Area of a square = ( 8 )² × (√2 )²

• Area of a square = ( 8 × 8 ) × (√2 )²

• Area of a square = 64 × 2

• Area of a square = 128 cm²

Area of shaded region = Area of a circle - Area of a square

• Area of shaded region = ( 200.1 - 128 ) cm²

• Area of shaded region = 72.1 cm²

∴ The area of shaded region ≈ 72 cm²

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