PSLE Gabriel 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 84 cm. The radius of each small quarter circle is 28 cm.
- What is the perimeter of the shaded part?
- What is the area of the shaded part?
(a)
Radius of the large quarter circle
= 84 - 28
= 56 cm
Perimeter of the large quarter circle
=
14 x 2 x
227 x 56
= 88 cm
Perimeter of 2 small quarter circles
=
12 x 2 x
227 x 28
= 88 cm
Difference in the radii between the large quarter circle and the small quarter circle
= 56 - 28
= 28 cm
Perimeter of the shaded part
= 28 + 28 + 28 + 28 + 88 + 88
= 288 cm
(b)
Area of the two quarter circles
= 2 x
14 x
227 x 28 x 28
= 1232 cm
2 Area of the boomerang
= 56 x 56 -
14 x
227 x 56 x 56
= 3136 - 2464
= 672 cm
2 Area of the shaded part
= 1232 + 672
= 1904 cm
2 Answer(s): (a) 288 cm; (b) 1904 cm
2