Question

Calculate the area of the shaded part of the square

Answer 1

area of the shaded part is 60.73 cm²

Explanation:

Find the area of square:

→ Length² → 10² → 100 cm²

Find area of circle:

→ πr² → 5²π → 25π

Find the area of semi circle

→ 25π ÷ 2 → 12.5π

the part inscribed in the square is half of the semi circle:

→ 12.5π ÷ 2 → 6.25π

the other semi circle is same as this one, so total area:

→ 6.25π + 6.25π = 12.5π cm²

now the area of shaded: 100 cm² - 12.5π cm²

→ 60.73 cm²

Answer 2

60.7 cm² (nearest tenth)

Explanation:

Square

From inspection of the diagram, we can determine that the side length of the square is 2 radii = 2 x 5cm = 10cm

Area of a square = side length x side length

⇒ area of square ABCD = 10 x 10 = 100 cm²

Square overlapping circle

All angles in a square measure 90°. Therefore, interior angle A and angle B of the square = 90°

Angles around a point add up to 360°. Therefore, the area of the square overlapping the circle = 360/90 = 1/4 of the area of the circle.

Area of a circle =
`\pi`r²

⇒ area of sector = 1/4 area of circle

= (1/4)
`\pi`r²

= (1/4)
`\pi`5²

= (1/4)
`\pi` x 25

= (25/4)
`\pi`

Shaded area

Shaded area = area of square - [2 x (1/4) area of circle]

= 100 - [2 x (25/4)
`\pi`]

= 100 - (25/2)
`\pi`

= 60.73009183...

= 60.7 cm² (nearest tenth)