Class 7 Maths Chapter 9 Practice Question Answers - Perimeter and Area

Q1. The area of a circle is the measurement of the region enclosed by its
(a) Radius
(b) Centre
(c) Circumference
(d) Area
Ans: (c)
Sol: As shown in the above figure, area is the region enclosed inside the boundary/circumference of the circle.

Q2. Circumference of a circle is ______
(a) πr
(b) 2πr
(c) 3πr
(d) 4πr
Ans: (b)
Sol: Circumference of a circle whose radius is r is given by 2πr.

Q3. Area of a circle is _______
(a) πr²
(b) 2π
(c) 2πr²
(d) 4πr
Ans: (a)
Sol: Area covered within the boundary of circle = π×r² , where r is a radius of a circle.

Q4. A path of width 8 m runs around a circular park whose radius is 38 m. Find the area of the path.
(a) 2112 m²
(b) 2834 m²
(c) 3212 m²
(d) 1578 m²
Ans: (a)
Sol: Inner radius (Radius of the park) =38 m
Outer radius (Radius of the park + path width of the park) =38+8=46 m
Area of the path =π(46² −38² )
= 22/7 (2116−1444)
= 22/7 (672)
=2112 m²

Q5. The radius of a circle is 5m. Find the circumference of the circle whose area is 49 times the area of the given circle.
(a) 220m
(b) 120m
(c) 320m
(d) 420m
Ans: (a)
Sol: Let's first find the area of the given circle with a radius of 5 meters:
Area of a circle = π × radius²
Area = π × 5² = π × 25 ≈ 78.54 square meters
Now, we are given that the area of another circle is 49 times the area of the given circle. So, the area of the second circle is:
Area of the second circle = 49 × 78.54 ≈ 3848.46 square meters
Now, we need to find the radius of the second circle:
Area of a circle = π × radius²
3848.46 = π × radius²
radius² = 3848.46 / π
radius ≈ √(3848.46 / π)
radius ≈ √(1225.98)
radius ≈ 35 meters (approximately)
Now, we can find the circumference of the second circle using the formula:
Circumference = 2 × π × radius
Circumference ≈ 2 × π × 35
Circumference ≈ 2 × 3.14 × 35
Circumference ≈ 220 meters
So, the circumference of the circle whose area is 49 times the area of the given circle is approximately 220 meters, and the correct answer is option (a)

Q6. The circumference of a circular field is 308m. Find its radius in metres.
(a) 49m
(b) 59m
(c) 91m
(d) 94m
Ans: (a)
Sol: The circumference of a circular field is 308m
Therefore, 2πr=308
⇒ r = 308 x 7 / 2 x 22
⇒ r = 49 m

Q7. The total boundary length of circle is called
(a) area
(b) volume
(c) circumference
(d) diameter
Ans: (c)
Sol: A circle is a two-dimensional shape, and it consists of all points in a plane that are equidistant from a fixed point called the center. The fixed distance from the center to any point on the circle is known as the radius (denoted by 'r').
The circumference of a circle is the total length of its boundary or outer edge. It is the distance you would travel if you were to walk around the entire circle along its edge. The circumference is directly related to the radius of the circle and is calculated using the formula:
Circumference ((c) = 2 × π × radius (r)
where π (pi) is an irrational constant approximately equal to 3.14159.

Q8. A circle is inscribed in a square as shown below. If the radius of the circle is 4 cm, then the perimeter of the square is ______

(a) 28 cm
(b) 24 cm
(c) 32 cm
(d) 36 cm
Ans: (c)
Sol: From the fig it is clear that,
Diameter of the circle = side of the square
So length of side of square  = 2 × 4 cm
 =8 cm
∴ perimeter of the square  = 8 + 8 + 8 + 8
=32 cm

Q9. Find the missing length of the following figure.

(a) 6 cm
(b) 4 cm
(c) 2 cm
(d) 5 cm
Ans: (a)
Sol: Let unknown side of the figure is x
Perimeter = sum of all sides of figure
23 = 4 + 5 + 8 + x
x = 23 − 17 = 6 cm.

Q10. Find the missing length of the figure given below.

(a) 4 cm
(b) 2 cm
(c) 6 cm
(d) 8 cm
Ans: (b)
Sol: Let unknown side is x
Perimeter = sum of length.
20 = 6 + 4 + 8 + x
x = 20 − 18 = 2 cm

 
Q11. If the radii of two concentric circles are 15 cm and 13 cm, respectively, then the area of the circulating ring in sq. cm will be:
(a) 176
(b) 178
(c) 180
(d) 200
Ans: (a)
Sol: R=15 cm,r=13 cm.

Area of the circulating ring = π(R² - r²)

Q12.Perimeter of a circle is called as__________
(a) Area
(b) Circumference
(c) Volume
(d) None of these
Ans: (b)
Sol: Perimeter of a circle is equal to its circumference i.e., P=2πr

Q13. Perimeter of a circle is called its _____
(a) radius
(b) area
(c) diameter
(d) none of these
Ans: (d)
Sol: Perimeter of a circle is called its circumference.

Q14. Perimeter of a triangle is the sum of the lengths of all the _____ sides.
(a) 4
(b) 2
(c) 3
(d) 6
Ans: (c)
Sol: Perimeter of a triangle is the sum of the lengths of all the three sides.

Q15. The radius of a wheel is 0.25m. How many rounds will it take to complete the distance of 11km?
(a) 7000
(b) 8000
(c) 9000
(d) 6000
Ans: (a)
Sol: Distance covered in one round = Circumference of wheel

Q16. The perimeter of a rectangle with length 8 cm and width 6 cm is:
(a) 26 cm
(b) 14 cm
(c) 20 cm
(d) 28 cm
Ans: (d)
Sol: Perimeter of a rectangle = 2 × (Length + Width)
= 2 × (8 cm + 6 cm)
= 2 × 14 cm
= 28 cm.

Q17. The area of a square with side length 5 cm is:
(a) 20 cm²
(b) 25 cm²
(c) 30 cm²
(d) 15 cm²
Ans: (b)
Sol: Area of a square = side × side
= 5 cm × 5 cm
= 25 cm².

Q18. A rectangular field has a length of 20 meters and a width of 15 meters. Its area is:
(a) 300 m²
(b) 400 m²
(c) 315 m²
(d) 200 m²
Ans: (a)
Sol: Area of a rectangle = Length × Width
= 20 m × 15 m
= 300 m².

Q19. The perimeter of a square is 24 cm. Its area is:
(a) 144 cm²
(b) 36 cm²
(c) 48 cm²
(d) 64 cm²
Ans: (b)
Sol: Let the side of the square be 's.' Perimeter = 4s = 24 cm
⇒ s = 24 cm / 4
= 6 cm.
Area of the square = side × side
= 6 cm × 6 cm
= 36 cm².

Q20. A rectangular garden is 12 meters long and 8 meters wide. Its perimeter is:
(a) 20 meters
(b) 32 meters
(c) 80 meters
(d) 40 meters
Ans: (b)
Sol: Perimeter of a rectangle = 2 × (Length + Width)
= 2 × (12 m + 8 m)
= 2 × 20 m
= 40 meters.

Q21. The length of a rectangle is 18 cm and its area is 108 cm². What is the width of the rectangle?
(a) 5 cm
(b) 6 cm
(c) 12 cm
(d) 10 cm
Ans: (b)
Sol: Let the width of the rectangle be 'w.'
Area of the rectangle = Length × Width
= 18 cm × w = 108 cm².
Solving for 'w,' we get
w = 108 cm² / 18 cm
= 6 cm.

Q22. The area of a triangle with base 10 cm and height 8 cm is:
(a) 18 cm²
(b) 40 cm²
(c) 80 cm²
(d) 32 cm²
Ans: (b)
Sol: Area of a triangle = (1/2) × base × height
= (1/2) × 10 cm × 8 cm
= 40 cm².

Q23. A rectangular room is 5 meters long and 4 meters wide. What is the area of the room in square meters?
(a) 20 m²
(b) 9 m²
(c) 16 m²
(d) 14 m²
Ans: (c) 20 m²
Sol: Area of a rectangle = Length × Width
= 5 m × 4 m
= 20 m².

Q24. The perimeter of an equilateral triangle is 30 cm. What is the length of each side?
(a) 10 cm
(b) 15 cm
(c) 12 cm
(d) 8 cm
Ans: (a)
Sol: Perimeter of an equilateral triangle = 3 × side length.
30 cm = 3 × side length.
Side length = 30 cm / 3 = 10 cm.

Q25. The area of a parallelogram with base 12 cm and height 8 cm is:
(a) 80 cm²
(b) 96 cm²
(c) 40 cm²
(d) 24 cm²
Ans: (b)
Sol: Area of a parallelogram = base × height
= 12 cm × 8 cm
= 96 cm².

Q26. A circular garden has a radius of 7 meters. What is the area of the garden in square meters? (Use π = 22/7)
(a) 154 m²
(b) 154 cm²
(c) 1540 m²
(d) 1540 cm²
Ans: (a)
Sol: Area of a circle = π × radius²
= (22/7) × 7 m × 7 m
= 154 m².

Q27. The perimeter of a regular hexagon is 48 cm. What is the length of each side?
(a) 12 cm
(b) 8 cm
(c) 6 cm
(d) 16 cm
Ans: (c)
Sol: Perimeter of a regular hexagon = 6 × side length. 48 cm
= 6 × side length. Side length
= 48 cm / 6
= 6 cm.

Q28. The length of a rectangle is 15 meters, and its area is 150 square meters. What is the width of the rectangle?
(a) 10 m
(b) 5 m
(c) 15 m
(d) 25 m
Ans: (b)
Sol: Let the width of the rectangle be 'w.'
Area of the rectangle = Length × Width
= 15 m × w = 150 m².
Solving for 'w,' we get
w = 150 m² / 15 m
= 10 m.

Q29. The perimeter of a square is 32 cm. What is the length of each side?
(a) 8 cm
(b) 16 cm
(c) 4 cm
(d) 64 cm
Ans: (a)
Sol: Perimeter of a square = 4 × side length.
32 cm = 4 × side length.
Side length = 32 cm / 4
= 8 cm.

Q30. The length of a rectangle is three times its width. If the width is 6 meters, what is the perimeter of the rectangle?
(a) 36 meters
(b) 18 meters
(c) 12 meters
(d) 24 meters
Ans: (d)
Sol: Let the width of the rectangle be 'w.'
Length = 3w. Perimeter = 2 × (Length + Width)
= 2 × (3w + 6 m)
= 2 × (3 × 6 m + 6 m)
= 2 × (18 m + 6 m)
= 2 × 24 m
= 24 meters.