Question

Find area of the shaded region if abcd is a square of side 28cm and apd and bpc are semicircles in a square

Answer 1

area of the shaded region if abcd is a square of side 28cm and apd and bpc are semicircles in a square is 20.57 cm^2

In the given figure, yellow colored portion represents the shaded portion.

• Area of shaded portion = Area of square - Area of semicircles
• = a^2 - [2 * π r^2/2]
• where,
• a is the side of a square
• "a" is the diameter of semicircle
• ∴ r = a/2 is the radius of semicircle.
• r = 28/2 = 16 cm
• given, a = 28 cm
• = 28^2 - [ 2 * π 16^2/2 ]
• = 784 - [ 256 π ]
• = 784 - [ 256 * 22/7]
• = 784 -   804.57
• = | - 20.57 |
• = 20.57 cm^2

Answer 2

Answer:

The Area of shaded portion is 168.56 sq cm .

Step-by-step explanation:

Given as :

ABCD is the square , each side of square = 28 cm

i.e AB = BC = CD = DA = 28 cm

APD and BPC is the semi-circle

Now, Area of square ABCD = side × side

Area of square ABCD = 28 cm × 28 cm

Or ,  Area of square ABCD = 784 sq cm

Again

The diameter of semi-circle = AD = 28 cm

So, the radius of semi-circle APD = $\dfrac{d}{2}$

Or,  r = $\dfrac{28}{2}$

∴    r = 14 cm

So, Area of semi-circle = π × $\dfrac{r^{2} }{2}$

Or. Area = 3.14 × $\dfrac{(14)^{2} }{2}$

or, Area = 3.14 × 98 = Area = 307.72  sq cm

So, The Area of semicircle with radius r = 307.72  sq cm

Again

The diameter of semi-circle = BC = 28 cm

So, the radius of semi-circle BPD = $\dfrac{d}{2}$

Or,  r' = $\dfrac{28}{2}$

∴    r' = 14 cm

So, Area of semi-circle = π × $\dfrac{r'^{2} }{2}$

Or. Area = 3.14 × $\dfrac{(14)^{2} }{2}$

or, Area = 3.14 × 98 = Area = 307.72  sq cm

So, The Area of semicircle with radius r' = 307.72  sq cm

Total Area of semicircle APD and BPC = 307.72  sq cm + 307.72  sq cm

∴ Total Area of semicircle APD and BPC = 615.44 sq cm

Now,

Area of shaded portion = Area of square ABCD - Total Area of semicircle APD and BPC

i.e Area of shaded portion = 784 sq cm - 615.44 sq cm

So,  Area of shaded portion = 168.56 sq cm

Hence, The Area of shaded portion is 168.56 sq cm . Answer