The figure is made up of a right-angled triangle BCD and two semicircles with BC and CD as their diameters respectively. The two semicircles and the line BD meet at E as shown. BC = 10 cm. CD = 24 cm and BD = 26 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 BEC
= ¹₂ x 3.14 x 10
= 15.7 cm

Circumference of Semicircle DEC
= ¹₂ x 3.14 x 24
= 37.68 cm

Perimeter of shaded region
= Circumference of semicircles + BD
= 15.7 cm + 37.68 cm + 26 cm
= 79.38 cm

(b)
Area of Triangle BCD
= ¹₂ x 24 x 10
= 120 cm²

Area of Semicircle BEC
= ¹₂ x 3.14 x 5 x 5
= 39.25 cm²

Area of Semicircle DEC
= ¹₂ x 3.14 x 12 x 12
= 226.08 cm²

Area of the shaded region
= 39.25 + 226.08 - 120
= 145.33 cm²

Answer(s): (a) 79.38 cm; (b) 145.33 cm²