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 42 cm. The radius of each small quarter circle is 14 cm.
- What is the perimeter of the shaded part?
- What is the area of the shaded part?
(a)
Radius of the large quarter circle
= 42 - 14
= 28 cm
Perimeter of the large quarter circle
=
14 x 2 x
227 x 28
= 44 cm
Perimeter of 2 small quarter circles
=
12 x 2 x
227 x 14
= 44 cm
Difference in the radii between the large quarter circle and the small quarter circle
= 28 - 14
= 14 cm
Perimeter of the shaded part
= 14 + 28 + 14 + 44 + 44
= 144 cm
(b)
Area of the two quarter circles
=
12 x
227 x 14 x 14
= 308 cm
2 Area of the boomerang
= 28 x 28 -
14 x
227 x 28 x 28
= 784 - 616
= 168 cm
2 Area of the shaded part
= 308 + 168
= 476 cm
2 Answer(s): (a) 144 cm; (b) 476 cm
2