Question

Please answer me the following questions of 12 ii part and iv part

Please tell me answers fast i need it for examination

Perimeter and area​

Answer 1

Questions

(i) Two semicircles of equal radii are cut out of a semicircular piece of cardboard. Find the area of the shaded portion.

(ii) Find the area of the shaded portion formed by a semicircle placed above a square.

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Answers

(i)

Given

• The diameter of the big semicircle is 14m
• The radius of small semicircle that is cut out of the big semicircle is 7m

To Find

• The area of the shaded area.

Solution

To find the area of the shaded area we must subtract the area of the bigger semicircle to the area of the smaller semicircles.

Area of the Bigger Semicircle ⇒ $\dfrac{\pi r^{2} }{2}$

(The radius would be 7 since the diameter is 14 and radius is equal to the half of the diameter)

⇒ $\dfrac{\frac{22}{7}\times (7)^{2} }{2}$

⇒ $\dfrac{\frac{22}{7}\times 49 }{2}$

⇒ $\dfrac{\frac{22}{7\div 7 }\times 49 \div 7 }{2}$

⇒ $\dfrac{22 \times 7 }{2}$

⇒ $\dfrac{154 }{2}$

⇒ $77$

∴ The area of the bigger semicircle is 77 m²

Area of smaller semicircle ⇒ $\dfrac{\pi r^{2} }{2}$

(The radius would be 3.5 since the diameter is 7 and radius is equal to the half of the diameter)

⇒ $\dfrac{3.14 \times (3.5)^{2} }{2}$

⇒ $\dfrac{3.14 \times 12.25}{2}$

⇒  $\dfrac{38.465}{2}$

⇒  $19.23$

∴ The area of the smaller semicircle is 19.23 m²

The area of the shaded part ⇒ Area of Bigger Semicircle - (Area of Smaller Semicircle × 2)

⇒ 77 - (19.23 × 2)

⇒ 77 - 38.46

⇒ 38.54

∴ The area of the shaded portion is 38.54 m²

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(ii)

Given

• Side of the square is 7 cm
• Diameter of semicircle is 7 cm

To Find

• The shaded area

Solution

To find the area of the shaded area we must add the area of the square to the area of the semicircle.

Area of Square ⇒ (Side)²

Area of Given Square ⇒ (7)² = 49

∴ The area of the given square is 49 cm²

Area of semicircle ⇒ $\dfrac{\pi r^{2} }{2}$

(The radius would be 3.5 since the diameter is 7 and radius is equal to the half of the diameter)

⇒ $\dfrac{3.14 \times (3.5)^{2} }{2}$

⇒ $\dfrac{3.14 \times 12.25}{2}$

⇒  $\dfrac{38.465}{2}$

⇒  $19.23$

∴ The area of the semicircle is 19.23 cm²

Now we must add the area of the square and semicircle.

49 + 19.23 = 69.23 cm²

∴ The area of the shaded portion is 69.23 cm²

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Answer 2

Answers (i)

Given :

• The diameter of the big semicircle is 14m

• The radius of small semicircle that is cut out of the big semicircle is 7m

To Find :

• Find the area of the shaded area

Solution :

$\boxed{\underline\text{ Area of the Bigger Semicircle} = \sf \: \dfrac{\pi r^{2} }{2}}$

Substitute all values :

$\sf : \implies \: \: \: \: \: \: \: \: \: \: \: \dfrac{\frac{22}{7}\times (7)^{2} }{2} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: \: \frac{ \frac{22}{7} \times 49}{2} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: \frac{\cancel{22 }\times 7}{ \cancel{2} }\\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: 11 \times 7 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: \: 77$

The area of the bigger semicircle is 77 m²

$\boxed{\underline\text{ Area of smaller semicircle } \sf \: \dfrac{\pi r^{2} }{2}}$

Substitute all values :

$\sf : \implies \: \: \: \: \: \: \: \: \dfrac{3.14 \times (3.5)^{2} }{2} \times 2 - 77\\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \frac{ \cancel{3.14} \times 12.25}{ \cancel{2}} \times 2 - 77\\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: 1.57 \times 12.25 \times 2 - 77 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \:19.23 \times 2 - 77\: \\ \\ \sf : \implies \: \: \: \: \: \: \: \:38.54$

The area of the shaded portion is 38.54 m²

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Answer (ii)

Given :

• Side of the square is 7 cm

• Diameter of semicircle is 7 cm

To Find :

• Find The shaded area

Solution :

$\underline{\boxed{ \text{Area of Square} \sf \: = \: (Side)^2}}$

Substitute all values :

$\text{Area of Square} \sf \: = \: (7)^2 \: \\ \\ \\ \text{Area of Square} \sf \: = \: 49 \:$

The area of the given square is 49 cm²

$\boxed{ \text{Area of semicircle } \sf \: = \: \dfrac{\pi r^{2} }{2}}$

Substitute all values :

$\sf : \implies \: \: \: \: \: \: \: \: \dfrac{3.14 \times (3.5)^{2} }{2} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \frac{ \cancel{3.14} \times 12.25}{ \cancel{2}} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: 1.57 \times 12.25 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \:19.23 \:$

The area of the semicircle is 19.23 cm²

Added the area of the square and semicircle.

$</p><p>\sf : \implies \: \: \: \: \: \: \: \: \:49 + 19.23 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \: 69.23 {</p><p>cm}^{2}$

The area of the shaded portion is 69.23 cm²