Worksheet Solutions: Area & Perimeter | Mathematics for Class 5 PDF Download

Q1: Madhavpur village has many fields. Find out the perimeter of the fields shown here:

1.
Ans: 
Rectangle:
Perimeter of a rectangle = 2 × (length + width)
Given dimensions: Length = 50 m, Width = 30 m
Perimeter = 2 × (50 m + 30 m) = 2 × 80 m = 160 m
Thus, the perimeters of the fields are: 160 meters

2.
Ans: Irregular Polygon:
Perimeter of an irregular polygon is the sum of all its sides.
Given side lengths: 8 m, 3 m, 7 m, 6 m, 5 m, 10 m
Perimeter = 8 m + 3 m + 7 m + 6 m + 5 m + 10 m = 39 m
Thus, the perimeters of the fields are: 39 meters

3.
Ans: Right Triangle:
Perimeter of a triangle = sum of all sides
Given side lengths: 40 m, 25 m, 10 m
Perimeter = 40 m + 25 m + 10 m = 75 m
Thus, the perimeters of the fields are: 75 meters

Q2: Find the perimeter of a rectangle whose sides are:
1. 3 cm and 6 cm
Ans: Perimeter = 2 × (length + width)
Rectangle with sides 3 cm and 6 cm: Perimeter = 2 × ( 3 cm + 6 cm ) = 2 × 9 cm = 18 cm

2. 15 cm and 9 cm
Ans: Perimeter = 2 × (length + width)
Rectangle with sides 15 cm and 9 cm: Perimeter = 2 × ( 15 cm + 9 cm ) = 2 × 24 cm = 48 cm

3. 7 cm and 9 cm
Ans: Perimeter = 2 × (length + width)
Rectangle with sides 7 cm and 9 cm: Perimeter = 2 × ( 7 cm + 9 cm ) = 2 × 16 cm = 32 cm 

Q3: Find the perimeter of the square whose side is:
1. 5 cm
Ans: Square with side 5 cm: Perimeter = 4 × 5 cm = 20 cm

2. 55 mm
Ans: Square with side 55 mm: Perimeter = 4 × 55 mm = 220 mm

3. 7 cm
Ans: Square with side 7 cm: Perimeter = 4 × 7 cm = 28 cm

Q4: Find the perimeter of the triangle whose sides are:
1. 2 cm, 4 cm and 5 cm
Ans: Triangle with sides 2 cm, 4 cm, and 5 cm: Perimeter = 2 cm + 4 cm + 5 cm = 11 cm

2. 3 cm, 4.5 cm and 5 cm
Ans: Triangle with sides 3 cm, 4.5 cm, and 5 cm: Perimeter = 3 cm + 4.5 cm + 5 cm = 12.5 cm

Q5: Find the perimeter of these shapes:

1. 

Ans: Shape 1 (Complex Polygon):

• It consists of smaller rectangles and squares, and I'll add up the outer edges since some internal measurements are provided that don't contribute directly to the perimeter.
• Perimeter = 4 cm (left vertical) + 2 cm (top horizontal) + 1 cm (top-right vertical) + 2 cm (top second horizontal) + 2 cm (right vertical) + 1 cm (bottom right horizontal) + 1 cm (bottom vertical) + 2 cm (bottom second horizontal) + 1 cm (bottom left vertical) + 2 cm (bottom third horizontal) + 2 cm (left second vertical)
• Perimeter = 4 + 2 + 1 + 2 + 2 + 1 + 1 + 2 + 1 + 2 + 2 = 20 cm

2.

Ans: Shape 2 (Pentagon):

• Perimeter of the pentagon = sum of all sides.
• Given side lengths: 4 cm, 4 cm, 8 cm, 8 cm, 6 cm
• Perimeter = 4 + 4 + 8 + 8 + 6 = 30 cm

3.
Ans: Shape 3 (Hexagon):

• Perimeter of the hexagon = sum of all sides.
• Given side length for each side: 5 cm
• Perimeter = 5 cm × 6 = 30 cm

Q6: Find the area of the following shaded figures. Here each small square represents 1 sq cm:
1.
Ans: Shaded Area for Figure:

• Count the number of squares horizontally and vertically within the shaded area.
• From the image, it appears the width is 4 squares (between points L and M), and the height is 3 squares (between points O and N).
• Area = Width × Height = 4 squares × 3 squares = 12 sq cm

2.

Ans: Shaded Area for Figure:

• Count the number of squares horizontally and vertically within the shaded area.
• From the image, it appears the width is 5 squares (between points A and B), and the height is 4 squares (between points D and C).
• Area = Width × Height = 5 squares × 4 squares = 20 sq cm

Q7: Find the area of the following squares:
1.

Ans: Square with side 12 cm: Area = 12 cm × 12 cm = 144 cm²

2.

Ans: Square with side 15 cm: Area = 15 cm × 15 cm = 225 cm²

Q8: Find the area of the following rectangles:
1.

Ans: Rectangle with dimensions 15 cm by 10 cm: Area = 15 cm × 10 cm = 150 cm²

2.

Ans: Rectangle with dimensions 5 cm by 2 cm: Area = 5 cm × 2 cm = 10 cm²

Q9: Find the area of the following rectangles with sides:
1. 1 m and 75 cm
Ans: Rectangle with sides 1 m and 75 cm: 
Convert 75 cm to meters: 75 cm = 0.75 m 
Area = 1 m × 0.75 m = 0.75 m²

2. 125 m and 84 m
Ans: Rectangle with sides 125 m and 84 m: 
Area = 125 m × 84 m = 10 , 500 m²

3. 32 m and 25 m
Ans: Rectangle with sides 32 m and 25 m: 
Area = 32 m × 25 m = 800 m²

Q10: Find the area of square with sides:
1. 40 m
Ans: Square with side 40 m: Area = 40 m × 40 m = 1600 m²

2. 24 cm
Ans: Square with side 24 cm: Area = 24 cm × 24 cm = 576 cm² 

Q11: Solve:
1. Find the perimeter of the rectangular Flower bed which is 56 m long and 29 m broad. Also, find its area.
Ans: Rectangular Flower Bed:
Perimeter of a rectangle = 2 × (length + width)
Area of a rectangle = length × width
Given Dimensions: Length = 56 m, Width = 29 m
Perimeter = 2 × (56 m + 29 m) = 2 × 85 m = 170 m
Area = 56 m × 29 m = 1624 m²

2. Reena bought a carpet 12 m long and 7 m broad. Find its area and perimeter.
Ans: Carpet Owned by Reena: 
Area of a rectangle = length × width 
Perimeter of a rectangle = 2 × ( length + width )
Given dimensions: Length = 12 m, Width = 7 m 
Area = 12 m × 7 m = 84 m²
Perimeter = 2 × ( 12 m + 7 m ) = 2 × 19 m = 38 m

3. The side of a square field is 8 m. If a person walks around it only once, find the total distance he has to cover. Also, find the area of the field.
Ans: Square Field: 
Perimeter of a square = 4 × side
Area of a square = side²
Given side length: 8 m 
Perimeter = 4 × 8 m = 32 m (This is the total distance a person has to cover if they walk around it once.) 
Area = 8 m × 8 m = 64 m²

Q12: Find the area of the figures drawn on 1 cm squared paper by counting the squares:
1.
Ans: Triangle:

• Count the number of complete squares inside the triangle plus estimate the portions of squares to approximate the area.
• Estimate from the image: Full squares = around 10, Partial squares = roughly equivalent to 4 full squares.
• Total area ≈ 14 sq cm.

2.
Ans: Triangle:

• This triangle seems smaller; count the full and partial squares.
• Estimate from the image: Full squares = around 6, Partial squares = roughly equivalent to 3 full squares.
• Total area ≈ 9 sq cm.

3.
Ans: Complex Irregular Shape:

• Count the full squares and make an educated guess on the partial squares.
• Estimate from the image: Full squares = around 8, Partial squares = roughly equivalent to 2 full squares.
• Total area ≈ 10 sq cm.

4.
Ans: Another Irregular Shape:

• Estimate from the image: Full squares = around 6, Partial squares = roughly equivalent to 2 full squares.
• Total area ≈ 8 sq cm.

5.
Ans: Curved Line Shape (seems to show just the path, not a filled area):

• If the task is to estimate the area under the curve, then consider the line as a boundary for an irregular area.
• Estimate from the image: Full squares = around 2, Partial squares = roughly equivalent to 1 full square.
• Total area ≈ 3 sq cm.

Q13: Find the area of the figures given below:

1.
Ans: T-Shape
Divide into two rectangles:

• Top Rectangle: 27 cm (length) × 3 cm (width) = 81 sq cm
• Bottom Rectangle (including the stem of the T): 7 cm (length) × 3 cm (width) = 21 sq cm

Total Area = 81 sq cm + 21 sq cm = 102 sq cm

2.
Ans: Complex Figure
Divide into three rectangles:

• Top Rectangle: 6 m (length) × 1 m (width) = 6 sq m
• Middle Rectangle: 2 m (length) × 2 m (width) = 4 sq m
• Bottom Rectangle: 4 m (length) × 1 m (width) = 4 sq m

Total Area = 6 sq m + 4 sq m + 4 sq m = 14 sq m

3.
Ans: U-Shape
Calculate total rectangle and subtract the inner rectangle:

• Total Outer Rectangle: 7 cm (length) × 3 cm (width) = 21 sq cm
• Inner Rectangle: 3 cm (length) × 1 cm (width) = 3 sq cm

Total Area = 21 sq cm - 3 sq cm = 18 sq cm

Q14: A rectangle has length 5 cm and breadth 4.5 cm and a square has each side 5 cm. Which figure has greater area and by how much?
Ans: 

1. Area of the Rectangle:

   • Formula: Area = length × breadth
   • Given: Length = 5 cm, Breadth = 4.5 cm
   • Area = 5 cm × 4.5 cm = 22.5 cm²

2. Area of the Square:

   • Formula: Area = side × side
   • Given: Side = 5 cm
   • Area = 5 cm × 5 cm = 25 cm²

To find out which has the greater area and by how much:

• The square has an area of 25 cm², and the rectangle has an area of 22.5 cm².
• Difference in area = Area of square - Area of rectangle = 25 cm² - 22.5 cm² = 2.5 cm²

Therefore, the square has a greater area by 2.5 cm² compared to the rectangle.

Q15: Find the perimeter of the following shapes:

1.
Ans: Rectangular L-Shape 
For this L-shaped figure, add up all the visible sides. The structure can be understood by tracing the entire outline: 
2 cm + 2 cm + 2 cm + 2 cm + 2 cm + 2 cm + 2 cm + 2 cm
Perimeter = 16 cm 16 cm

2.
Ans: Irregular Pentagon 
This shape has each side length given: 
Perimeter = 7 cm + 5 cm + 6 cm + 4 cm + 3 cm + 2 cm
Perimeter = 27 cm 27 cm

Q16: Find the area of the following shapes:

Ans: The L-shaped figure can be divided into two rectangles. Calculate each rectangle's area and sum them:

• Rectangle 1: 10 cm (length) × 3 cm (width) = 30 sq cm
• Rectangle 2 (above the longer rectangle): 4 cm (length) × 2 cm (width) = 8 sq cm
• Total Area = 30 sq cm + 8 sq cm = 38 sq cm

Q17: Find the area of the following shapes by counting the unit squares:

Ans: For the triangle drawn within the grid, count the number of 1 sq cm units:

• It appears the triangle is a right triangle with a base and height along the grid lines.
• Count of full and partial squares to estimate the area visually.
• Estimate from visual: Base of the triangle = 10 units, Height = 5 units.
• Area of a triangle = 0.5 × base × height = 0.5 × 10 × 5 = 25 sq cm

Q18: Answer the following questions:
1. The length of a field is 40 m and breadth is 25 m. Find the area of the field? Also, find the length of the boundary of the field.
Ans: Area and Perimeter of a Field Area = Length × Breadth = 40 m × 25 m = 1000 m²
Perimeter = 2 × (Length + Breadth) = 2 × (40m + 25m) = 2 × 65m = 130m

2. What will be the labor charge for tiling a hall 22 m long and 17 m wide at the rate of ₹ 8 per sq m?
Ans: Labor Charge for Tiling a Hall 
Area of the Hall = Length × Width = 22 m × 17 m = 374 m²
Labor Charge = Area × Rate per sq m = 374 m² × ₹ 8 / m² = ₹ 2992

Q19: Perimeter of a square = ______.
Ans: Perimeter of a square = 4 × side length

Q20: Find the perimeter of the square whose area is 16 m². ______.
Ans: Given the area of the square = 16 m²

Perimeter = 4 × side length = 4 × 4 m = 16 m