Area and perimeter Questions and answers

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Elementary Mathematics

71). Find the area of the largest circle that can be drawn inside a rectangle with sides 18 cm and 14 cm.

A). 49 sq cm

B). 154 sq cm

C). 378 sq cm

D). 1078 sq cm

View Answer

72). The area of a square is twice the area of a circle. The area of the circle is 392 sq cm. Find the length of the side of the square.

A). 28 cm

B). 26 cm

C). 24 cm

D). 22 cm

View Answer

73). The area of a rectangle is equal to the area of a circle with circumference equal to 39.6 m. What is the length of the rectangle if its breadth is 4.5 m?

A). 33.52 m

B). 21.63 m

C). 31.77 m

D). 27.72 m

View Answer

Correct Answer: 27.72 m

Let the radius of the circle be r.

Perimeter of given circle = 39.6 m

\( \Large 2\pi r \)=39.6 => =\( \Large \frac{7\times 39.6}{22\times 2} \)=6.3m

Area of circle = \( \Large \frac{22}{7}\times 6.3\times 6.3 \)

= \( \Large \frac{873.18}{7}=124.74 m^{2} \)

Now, area of a rectangle = Area of a circle

\( \Large l\times b \)=124.74 => \( \Large l\times 4.5 \)=124.74

l=\( \Large \frac{124.74}{4.5} \)=27.72 m.

74). Area of circle is equal to the area of a rectangle having perimeter of 50 cm and the length is more than its breadth by 3cm. What is the diameter of the Circle?

A). 7 cm

B). 21 cm

C). 28 cm

D). 14 cm

View Answer

Correct Answer: 14 cm

Let breadth of the rectangle be b.

Then, length = (b + 3)

According to the question,

2(b+b+3)=50 => 2b+3=25

=> 2b=22 => b=\( \Large \frac{22}{2} \)=11

Breadth = 11 cm

Length = (11 + 3) = 14 cm

Area of the circle = Area of the rectangle

=> \( \Large \pi r^{2}=14\times 11 \)

=> \( \Large r^{2} \)=\( \Large \frac{14\times 11\times 7 }{22} \)=49

r=\( \Large \sqrt{49} \)=7 cm.

Diameter=2r=\( \Large 2\times 7 \)=14 cm.

75). The area of a rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3 rd of the side of the square. What is the side of the square?

A). 10 cm

B). 20 cm

C). 15 cm

D). Couldn't be determined

View Answer

76). The area of a rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3 rd of the side of the square. What is the side of the square?

A). 10 cm

B). 20 cm

C). 9 cm

D). Cannot be determined

View Answer

77). The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cm and 43 cm, respectively. What is the half the radius of the circle?

A). 56 cm

B). 14 cm

C). 28 cm

D). 15 cm

View Answer

Correct Answer: 14 cm

According to the question,

\( \Large 2\pi r \)=2(45+43)=\( \Large 2\times 88 \)

=> r=\( \Large \frac{2\times 88 }{2\pi} \)

\( \Large \frac{1}{2}r \)=\( \Large \frac{2\times 88\times 7}{2\times 44} \)=14 cm.

78). If the area of a circle is equal to the area of square with side \( \Large \Large 2\sqrt{\pi} \) units, what is the diameter of the circle ?

A). 1 unit

B). 2 units

C). 4 units

D). 8 units

View Answer

Correct Answer: 4 units

Area of the circle = Area of the square

=\( \Large (Side)^{2} \)

\( \Large \pi r^{2}=(2\sqrt{\pi})^{2} \)

=> \( \Large \pi r^{2}=4\pi \)

=> \( \Large r^{2}=\frac{4\pi}{\pi} \)=4

=> r=\( \Large \sqrt{4} \)=2 units

Diameter of circle (d) = \( \Large 2\times r=2\times 2 \)

= 4 units

79). If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct?

A). Area of circle = Area of square

B). \( \Large Area \ of \ circle \ge \ Area \ of \ square \)

C). Area of circle > Area of square

D). Area of circle < Area of square

View Answer

Correct Answer: Area of circle > Area of square

Let the radius of a circle is r and a be the length of the side of a square.

Given, circumference of a circle = Perimeter of a square

=> \( \Large 2\pi r \)=4a

=> a=\( \Large \frac{\pi }{2}r \)=1.57r

Now, area of the circle \( \Large (A_{c}) \)=\( \Large \pi r^{2}=3.14 r^{2} \)

and area of the square

\( \Large (A_{s})=a^{2}=2.4649 r^{2} \)

Area of circle > Area of square.

80). Consider the following statements.
The area of square is greater than the area of the triangle.
The area of circle is less than the area of triangle.
Which of the statement is/are correct?

A). Only I

B). Only II

C). Both l and II

D). Neither I nor II

View Answer

Correct Answer: Only I

Let the radius of circle is 'r' and a side of a square is 'a', then given condition

\( \Large 2\pi r \)=4a => a=\( \Large \frac{\pi r}{2} \)

Area of square

=\( \Large \left(\frac{\pi r}{2}\right)^{2}=\frac{\pi^{2}r^{2}}{4}=\frac{9.86 r^{2}}{4}=2.46 r^{2} \)

and area of circle = \( \Large \pi r^{2}=3.14 r^{2} \)

and let the side of equilateral triangle is x.

Then, given condition,

3x=\( \Large 2\pi r \)=> x=\( \Large \frac{2\pi r}{3} \)

Area of equilateral triangle = \( \Large \frac{\sqrt{3}}{4}x^{2} \)

=\( \Large \frac{\sqrt{3}}{4}\)\( \Large \times \)\( \Large \frac{4\pi^{2}r^{2}}{9} \)

=\( \Large \frac{\pi^{2}}{3\sqrt{3}}r^{2}=1.89 r^{2} \)

Hence, Area of circle > Area of square > Area of equilateral triangle.

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