Worksheet Solutions: Perimeter and Area - 1

Multiple Choice Questions

Q1: What is the perimeter of a rectangle with a length of 15 cm and a width of 10 cm?
(a) 25 cm
(b) 30 cm
(c) 40 cm
(d) 50 cm
Ans: (d) 50 cm
Solution: The perimeter is 2 × (length + width) = 2 × (15 cm + 10 cm) = 50 cm.

Q2: A square has a perimeter of 24 cm. What is the length of one side?
(a) 4 cm
(b) 6 cm
(c) 8 cm
(d) 12 cm
Ans: (b) 6 cm
Solution: The side length is perimeter ÷ 4, so 24 cm ÷ 4 = 6 cm.

Q3: The area of a rectangle is 54 square units. If its length is 9 units, what is its width?
(a) 5 units
(b) 6 units
(c) 7 units
(d) 8 units
Ans: (b) 6 units
Solution: The width is area ÷ length, so 54 square units ÷ 9 units = 6 units.

Q4: A triangle has a perimeter of 20 cm. If two of its sides are 8 cm and 6 cm, what is the length of the third side?
(a) 4 cm
(b) 6 cm
(c) 8 cm
(d) 10 cm
Ans: a) 6 cm
Solution: The third side is calculated by subtracting the sum of the other two sides from the perimeter: 20 cm - (8 cm + 6 cm) = 6 cm.

Q5: A rectangular park is 30 meters long and 20 meters wide. What is the area of the park?
(a) 50 square meters
(b) 100 square meters
(c) 400 square meters
(d) 600 square meters
Ans: d) 600 square meters
Solution: The area is length × width, so 30 meters × 20 meters = 600 square meters.

Fill in the Blanks

Q1: The perimeter of a square with a side length of 5 cm is _______.
Ans: 20 cm
Solution: The perimeter of a square is calculated as 4 × side length, so 4 × 5 cm = 20 cm.

Q2: A rectangular field has a length of 10 m and a width of 5 m. The perimeter of the field is _______.
Ans: 30 m
Solution: The perimeter of a rectangle is 2 × (length + width), so 2 × (10 m + 5 m) = 30 m.

Q3: If the area of a square is 64 square units, the length of one side is _______ units.
Ans: 8 units
Solution: The area of a square is side length × side length, so the side length is √64 = 8 units.

Q4: The perimeter of a triangle with sides of 7 cm, 8 cm, and 9 cm is _______.
Ans: 24 cm
Solution: The perimeter of a triangle is the sum of the lengths of its sides, so 7 cm + 8 cm + 9 cm = 24 cm.

Q5: A rectangular garden has an area of 48 square meters and a width of 6 meters. The length of the garden is _______ meters.
Ans: 8 meters
Solution: The area of a rectangle is length × width, so 48 square meters ÷ 6 meters = 8 meters.

True/False

Q1: The area of a rectangle is always greater than its perimeter.
Ans: False
Solution: The area of a rectangle depends on its length and width, and can be less than, equal to, or greater than the perimeter depending on the dimensions.

Q2: The perimeter of a square is four times the length of one side.
Ans: True
Solution: The formula for the perimeter of a square is 4 × side length.

Q3: A triangle with all sides equal has a perimeter that is three times the length of one side.
Ans: True
Solution: The perimeter of an equilateral triangle is 3 × side length.

Q4: If a rectangle has an area of 36 square units and a width of 4 units, its length must be 9 units.
Ans: True
Solution: The length is calculated as area ÷ width, so it should be 36 ÷ 4 = 9 units.

Q5: A square and a rectangle with the same perimeter have the same area.
Ans: False
Solution: The area of the shapes depends on the side lengths, so they can have different areas even if the perimeter is the same.

Answer the following Questions 

Q1: Draw a square with a side length of 5 units. Calculate its perimeter and area.
Ans:Perimeter = 20 units, Area = 25 square units
Solution: The perimeter is 4 × side length = 4 × 5 units = 20 units. The area is side length × side length = 5 units × 5 units = 25 square units.

Q2: A square-shaped playground has a side length of 150 m. The cost of fencing the playground is ₹12 per meter. What will be the total cost of fencing?

Ans: ₹7,200
Solution:
Perimeter of a square = 4 × side
= 4 × 150
= 600 m

Cost per meter = ₹12
Total cost = 600 × 12
= ₹7,200

Q3: A farmer wants to plant a rectangular field with a length of 100 meters and a width of 40 meters. What is the area of the field?
Ans: 4000 square meters
Solution: The area is length × width = 100 meters × 40 meters = 4000 square meters.

Q4: A rectangular parking area is 120 m long and 60 m wide. If each car requires 20 sq. m of space, what is the maximum number of cars that can be parked in the area?

Ans: 360 cars

​Solution:
Area of the parking lot = 120 × 60 = 7,200 sq. m
Each car requires 20 sq. m
Maximum number of cars = 7200 ÷ 20
= 360 cars

Q5: Draw a rectangle with a length of 8 units and a width of 4 units. Calculate the perimeter and area.
Ans: 

Perimeter = 24 units, Area = 32 square units
Solution: The perimeter is 2 × (length + width) = 2 × (8 units + 4 units) = 24 units. The area is length × width = 8 units × 4 units = 32 square units.