CBSE Class 5 Mathematics Area and Perimeter Assignment

TOPIC: AREA AND PERIMETER

Part (1)

Sub topic: Perimeter

Rectilinear figure
A plane figure made of line segments is called a rectilinear figure. For example, a triangle, a quadrilateral etc. are rectilinear figures.

Perimeter of a Rectilinear figures:
Definition: The sum of all sides of a rectilinear figure is called its perimeter.
OR
The distance around the edge of a figure is its perimeter.

Explanation: Suraj needs to put a frame around the picture he has made. To find how much he needs to buy, he takes a string and wraps it around the picture with a knot in every corner. He then measures the string and finds that it is 90 cm long. The string shows the length of the frame or the distance around the picture. Thus the total length or the distance around the picture is its perimeter.

Note: Perimeter must always be expressed along with its units of length like cm, m etc. We use 1 unit to measure perimeter.

Question 1. Find the perimeter of the given triangle with sides 4cm, 7cm, and 6cm.
Answer: Perimeter = 4cm + 7cm + 6cm = 17cm
In simple words: The perimeter is found by adding the lengths of all three sides of the triangle together.

Exam Tip: Always include the unit of measurement (cm) in your final answer.

Question 2. Find the perimeter of the given shaded grid figure where each square has sides of 1cm (18 shaded squares).
Answer: There are 18 squares that are shaded.
Therefore, Perimeter = 18cm
In simple words: Count the outer boundary length by taking each square grid edge as 1cm.

Exam Tip: When counting grid perimeters, count the outer boundary segments rather than just the inner area squares.

Question 3. Use a centimetre ruler to find the perimeter of the cross-shaped figure with side lengths 3cm, 1cm, 1cm, 3cm, 1cm, 1cm, 3cm, 1cm, 1cm, 3cm, 1cm, and 1cm.
Answer: Perimeter = Sum of the length of all sides.
Perimeter = \(3\text{cm} + 1\text{cm} + 1\text{cm} + 3\text{cm} + 1\text{cm} + 1\text{cm} + 3\text{cm} + 1\text{cm} + 1\text{cm} + 3\text{cm} + 1\text{cm} + 1\text{cm} = 20\text{cm}\)
In simple words: Add up every individual outer edge segment around the shape to get the total perimeter.

Exam Tip: Tick off each side as you add it to ensure you do not miss any side or count any side twice.

Question 4. Find the missing length of the figure with given sides 4cm, 1cm, 3cm, 5cm, and a missing side, given that the total perimeter is 20cm.
Answer: Perimeter = 20cm
Sum of the lengths of the four known sides = \(4\text{cm} + 1\text{cm} + 3\text{cm} + 5\text{cm} = 13\text{cm}\)
Length of the missing (fifth) side = Perimeter - Sum of the lengths of the four sides
\(= 20\text{cm} - 13\text{cm} = 7\text{cm}\)
In simple words: Subtract the sum of the known sides from the total perimeter to find the missing side length.

Exam Tip: Double-check your addition of the known sides before subtracting from the total perimeter.

Question 5. How much wire does Ahmad need to fence a garden with side lengths 9m, 12m, and 10m?
Answer: Perimeter of this garden = \(9\text{m} + 12\text{m} + 10\text{m} = 31\text{m}\)
Therefore, Ahmad needs 31m wire to fence the garden.
In simple words: Fencing requires covering the entire boundary, which is equal to the perimeter of the garden.

Exam Tip: Word problems involving fencing, framing, or running around a track always ask for the perimeter.

Question 6. How much distance did Rajesh cover if he has taken 5 rounds around the playground of dimensions 7cm by 5cm?
Answer: Perimeter of the playground = \(7\text{cm} + 5\text{cm} + 7\text{cm} + 5\text{cm} = 24\text{cm}\)
No. of rounds taken = 5
Distance covered in 1 round = 24cm
Distance covered in 5 rounds = \(24 \times 5 = 120\text{cm}\)
Therefore, Rajesh covered 120cm in 5 rounds.
In simple words: Multiply the perimeter of one round by the total number of rounds taken.

Exam Tip: When multiple rounds are taken, first find the perimeter for one round and then multiply by the number of rounds.

Part (2)

Sub topic: Perimeter of Rectangle and Square

Perimeter of a Rectangle:
Let us consider a rectangle with length = 6cm and breadth = 4cm.
Perimeter of Rectangle = 2 times (sum of length and breadth)
\(= 2 \times (l + b)\)
\(= 2 \times (6\text{cm} + 4\text{cm})\)
\(= 2 \times 10\text{cm} = 20\text{cm}\)

Perimeter of a Square:
Let us consider a square with side = 3cm.
Perimeter of square = 4 times (length of each side)
\(= 4 \times 3\text{cm} = 12\text{cm}\)

Perimeter (Worksheet-1)

Q1. Find the perimeter of the given figures (Rectangle with length 6cm and breadth 3cm, and Rectangle with length 5cm and breadth 4cm).
Answer:
For the first rectangle (length = 6cm, breadth = 3cm):
Perimeter = \(2 \times (\text{length} + \text{breadth})\)
\(= 2 \times (6\text{cm} + 3\text{cm})\)
\(= 2 \times 9\text{cm} = 18\text{cm}\)
For the second rectangle (length = 5cm, breadth = 4cm):
Perimeter = \(2 \times (5\text{cm} + 4\text{cm})\)
\(= 2 \times 9\text{cm} = 18\text{cm}\)
In simple words: Add length and breadth, then multiply by 2 for each rectangle.

Exam Tip: You can also find rectangle perimeter by adding all four sides: \(\text{length} + \text{length} + \text{breadth} + \text{breadth}\).

Q2. Find the perimeter of the given square cardboard with side 2cm.
Answer: Perimeter of square = \(4 \times \text{side}\)
\(= 4 \times 2\text{cm} = 8\text{cm}\)
In simple words: Multiply the side length of the square by 4.

Exam Tip: Since all four sides of a square are equal, multiplying the side by 4 is faster than adding it four times.

Q3. Find the perimeter of the rectangle whose length is 20m and breadth is 15m.
Answer: Perimeter of rectangle = \(2 \times (\text{length} + \text{breadth})\)
\(= 2 \times (20\text{m} + 15\text{m})\)
\(= 2 \times 35\text{m} = 70\text{m}\)
In simple words: Add 20m and 15m, then multiply the sum by 2.

Exam Tip: Always write the formula before substituting the values to secure step-marking points.

Q4. The perimeter of a square is 408m. Find the length of each side of a square.
Answer: Perimeter of square = \(4 \times \text{side}\)
Length of each side = \(\frac{\text{Perimeter}}{4}\)
\(= \frac{408\text{m}}{4} = 102\text{m}\)
In simple words: Divide the total perimeter by 4 to find the length of one side of the square.

Exam Tip: When perimeter is given and side is required, always divide by 4 for squares and by 2 for semi-perimeters.