PSLE
Sam designed a logo as shown. The logo is made up of 2 small identical quarter circles, a large quarter circle and two straight lines drawn inside a square of side 21 cm. The radius of each small quarter circle is 7 cm.

1. What is the perimeter of the shaded part?
2. What is the area of the shaded part?

(a)
Radius of the large quarter circle
= 21 - 7
= 14 cm

Perimeter of the large quarter circle
= ¹₄ x 2 x ²²₇ x 14
= 22 cm

Perimeter of 2 small quarter circles
= ¹₂ x 2 x ²²₇ x 7
= 22 cm

Difference in the radii between the large quarter circle and the small quarter circle
= 14 - 7
= 7 cm

Perimeter of the shaded part
= 7 + 7 + 7 + 7 + 22 + 22
= 72 cm

(b)
Area of the two quarter circles
= 2 x ¹₄ x ²²₇ x 7 x 7
= 77 cm²

Area of the boomerang
= 14 x 14 - ¹₄ x ²²₇ x 14 x 14
= 196 - 154
= 42 cm²

Area of the shaded part
= 77 + 42
= 119 cm²

Answer(s): (a) 72 cm; (b) 119 cm²