Question

In the given figure, AB = 1/2BC, where BC = 14 cm (Use π = 22/

7

). Find:

(i) Area of quad. AEFD

(ii) Area of ABC

(iii) Area of semicircle.

Hence find the area of shaded region.​

Answer 1

(i) Area of quad. AEFD = 196 cm²

(ii) Area of ∆ABC = 49 cm²

(iii) Area of semicircle = 77 cm²

Area of shaded region = 70 cm²

The area of ∆ABC = 1/2 x AB × BC

( Using the formula area = 1/2 base x height for a right angled triangle)

AB = BC /2 (given) = 7cm

=> Area = 1/2 x 7 x 14

=> 49 cm2

Area of ∆ABC = 49 cm²

The quadrilateral AEFD is a square as all the sides are equal i.e, equal to 14 cm -

The area of AEFD = 14 x 14

=> 196 cm²

The semicircle has a diameter BC = 14 cm and radius = 7 cm.

Area= π (radius)²

=> 22/7 x 49/2

=> 77 cm²

Area of the semicircle = 77cm²

Area of shaded region = 196 - 77 - 49

= 70 cm²

Answer 2

Area of Quadrilateral AEFD = 196 cm² ,Area of A ABC =49 cm², Area of Semi Circle = 77 cm², Area of Shaded region = 70 cm² Step-by-step explanation: BC = 14 cm AB=BC/2 = 14/2 = 7 cm BC Diameter = 14 cm BE = Radius = 7 cm AE = AB + BE = 7+7= 14 cm AD = EF = BC = 14 cm Area of Square AEFD = 14 * 14 = 196 cm² Area of A ABC = (1/2) 14* 7 = 49 cm² Area of Semi Circle = (1/2)π R² = (1/2) (22/7) * 7² = 77 cm² Area of Shaded region = 196 - 49 - 77 = 70