The figure is made up of a right-angled triangle HKL and two semicircles with HK and KL as their diameters respectively. The two semicircles and the line HL meet at N as shown. HK = 12 cm. KL = 16 cm and HL = 20 cm. (Take π = 3.14)
- Find the perimeter of the shaded region. Correct the answer to 2 decimal places.
- Find the area of the shaded region.
(a)
Circumference of Semicircle HNK
=
12 x 3.14 x 12
= 18.84 cm
Circumference of Semicircle LNK
=
12 x 3.14 x 16
= 25.12 cm
Perimeter of shaded region
= Circumference of semicircles + HL
= 18.84 cm + 25.12 cm + 20 cm
= 63.96 cm
(b)
Area of Triangle HKL
=
12 x 16 x 12
= 96 cm
2 Area of Semicircle HNK
=
12 x 3.14 x 6 x 6
= 56.52 cm
2 Area of Semicircle LNK
=
12 x 3.14 x 8 x 8
= 100.48 cm
2 Area of the shaded region
= 56.52 + 100.48 - 96
= 61 cm
2 Answer(s): (a) 63.96 cm; (b) 61 cm
2