PSLE
Ian 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 63 cm. The radius of each small quarter circle is 21 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
= 63 - 21
= 42 cm

Perimeter of the large quarter circle
= ¹₄ x 2 x ²²₇ x 42
= 66 cm

Perimeter of 2 small quarter circles
= ¹₂ x 2 x ²²₇ x 21
= 66 cm

Difference in the radii between the large quarter circle and the small quarter circle
= 42 - 21
= 21 cm

Perimeter of the shaded part
= 21 + 42 + 21 + 66 + 66
= 216 cm

(b)
Area of the two quarter circles
= ¹₂ x ²²₇ x 21 x 21
= 693 cm²

Area of the boomerang
= 42 x 42 - ¹₄ x ²²₇ x 42 x 42
= 1764 - 1386
= 378 cm²

Area of the shaded part
= 693 + 378
= 1071 cm²

Answer(s): (a) 216 cm; (b) 1071 cm²