Question

The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part.

Answer 1

Explanation:

The total shaded area = area of the square - area of a circle

= 9^2 - π * 4.5^2

= 17.3827

The 2 shaded parts both have area 8.69 unit^2 ( to nearest hundred)

Perimeter:

The perimeter of the top shaded part

= AB + 1/2 circmference of the circle

= 9 + 1/2 * 2 π r

= 9 + 14.137

= 23.14 units ( to nearest hundredth)

The bottom part has the same perimeter.

Answer 2

• area: 17.38 cm²
• perimeter: 46.27 cm

Explanation:

You want the perimeter and area of the part of a 9 cm square remaining after a semicircle is removed from two opposite sides.

Area

The shaded area is the area of the 9 cm square less the area of a 9 cm circle. That area is ...

A = s² - π(s/2)² = s²(1 -π/4) . . . . . where s is the side length of the square

A = (9 cm)²(1 -π/4) ≈ 17.38 cm²

The area is about 17.38 cm².

Perimeter

The perimeter is the circumference of the circle plus two sides of the square.

P = C +2s

P = πs +2s = s(π+2)

P = (9 cm)(π+2) ≈ 46.27 cm

The perimeter is about 46.27 cm.

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