The figure is made up of a right-angled triangle RST and two semicircles with RS and ST as their diameters respectively. The two semicircles and the line RT meet at U as shown. RS = 6 cm. ST = 8 cm and RT = 10 cm. (Take π = 3.14)

1. Find the perimeter of the shaded region. Correct the answer to 2 decimal places.
2. Find the area of the shaded region.

(a)
Circumference of Semicircle RUS
= ¹₂ x 3.14 x 6
= 9.42 cm

Circumference of Semicircle TUS
= ¹₂ x 3.14 x 8
= 12.56 cm

Perimeter of shaded region
= Circumference of semicircles + RT
= 9.42 cm + 12.56 cm + 10 cm
= 31.98 cm

(b)
Area of Triangle RST
= ¹₂ x 8 x 6
= 24 cm²

Area of Semicircle RUS
= ¹₂ x 3.14 x 3 x 3
= 14.13 cm²

Area of Semicircle TUS
= ¹₂ x 3.14 x 4 x 4
= 25.12 cm²

Area of the shaded region
= 14.13 + 25.12 - 24
= 15.25 cm²

Answer(s): (a) 31.98 cm; (b) 15.25 cm²