The figure is made up of a right-angled triangle DEF and two semicircles with DE and EF as their diameters respectively. The two semicircles and the line DF meet at G as shown. DE = 6 cm. EF = 8 cm and DF = 10 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 DGE
=
12 x 3.14 x 6
= 9.42 cm
Circumference of Semicircle FGE
=
12 x 3.14 x 8
= 12.56 cm
Perimeter of shaded region
= Circumference of semicircles + DF
= 9.42 cm + 12.56 cm + 10 cm
= 31.98 cm
(b)
Area of Triangle DEF
=
12 x 8 x 6
= 24 cm
2 Area of Semicircle DGE
=
12 x 3.14 x 3 x 3
= 14.13 cm
2 Area of Semicircle FGE
=
12 x 3.14 x 4 x 4
= 25.12 cm
2 Area of the shaded region
= 14.13 + 25.12 - 24
= 15.25 cm
2 Answer(s): (a) 31.98 cm; (b) 15.25 cm
2