Question

In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region. [Use pie = 3.14]

Answer 1

HERE IS THE SOLUTION FOR YOUR QUESTION;

◆ AED is an right angle triangle

AD2= AE2+ED2.

⇒ AD2 = (92+ 122)

= (81 + 144)

= 225 cm2

⇒ AD = 15 cm

◆Area of the rectangular region ABCD

= AB × AD

= (20 × 15)

= 300 cm2

◆Area of ∆AED

= 12× AE × DE = (12 × 9 × 12) cm2 = 54 cm2

In a rectangle

AD = BC = 15 cm

◆Since, BC is the diameter of the circle, radius of the circle = 15 cm◆

◆Area of the semi-circle = 1/2 × π × r2

= (1/2 × 3.14 × 15 × 15) = 88.3125 cm2

◆Area of the shaded region = Area of the rectangle + Area of the semi-circle − Area of the triangle◆

= (300 + 88.3125 − 54) cm2

= 334.31 cm2 .

HOPE IT HELPS