CBSE Class 5 Mathematics How Many Squares Worksheet Set 01

Question 1. Find the perimeter of the first figure (a rectangle made of 8 unit squares arranged in 2 rows of 4 columns, assuming each grid square has a side length of 1 unit).
Answer: Let the side length of each small grid square be 1 unit.
The shape consists of 2 rows and 4 columns of unit squares, forming a rectangle of length 4 units and breadth 2 units.
Perimeter = \(2 \times (\text{Length} + \text{Breadth})\)
Perimeter = \(2 \times (4 + 2) = 2 \times 6 = 12\) units.
In simple words: The perimeter is the total outer boundary length around the shape, which equals 12 units.
Exam Tip: Count the outer boundary edges carefully rather than adding all internal grid lines when finding perimeter.

Question 2. Find the perimeter of the second figure (a square grid of \(5 \times 5\) unit squares, assuming each small square has a side length of 1 unit).
Answer: Let the side length of each small grid square be 1 unit.
The grid consists of 5 rows and 5 columns, forming a large square of side length 5 units.
Perimeter of a square = \(4 \times \text{Side}\)
Perimeter = \(4 \times 5 = 20\) units.
In simple words: Multiply the length of one outer side of the grid by 4 to get the total perimeter of 20 units.

Exam Tip: For any regular grid or square figure, always use the overall outer dimensions to calculate the perimeter quickly.

Question 3. Find the area of the first figure (the arrow shape drawn on the grid).
Answer: To find the area of the arrow shape, count the full grid squares and half grid squares enclosed within the boundary.
Let each small grid square have an area of 1 square unit.
Counting the full squares and half squares inside the arrow:
Number of full squares = 6
Number of half squares (triangles formed by diagonals) = 4 (which equals \(4 \times 0.5 = 2\) full squares)
Total Area = \(6 + 2 = 8\) square units.
In simple words: Count all complete squares as 1 and two half-squares as 1 to find the total area of 8 square units.

Exam Tip: Always group half-squares into pairs to make whole units when counting area on grid paper.

Question 4. Find the area of the second figure (the right-angled triangle drawn on the grid).
Answer: The triangle is drawn on a grid where the base spans 4 units and the height spans 4 units.
Area of a triangle = \(\frac{1}{2} \times \text{Base} \times \text{Height}\)
Area = \(\frac{1}{2} \times 4 \times 4 = \frac{16}{2} = 8\) square units.
Alternatively, counting grid squares: It covers half of a \(4 \times 4\) square grid, so area = \(\frac{16}{2} = 8\) square units.
In simple words: The area of a right-angled triangle is half the area of the rectangle formed by its base and height, which is 8 square units.

Exam Tip: You can either use the triangle area formula or count the squares and half-squares directly from the grid for verification.

Please refer to attached file for CBSE Class 5 Maths Worksheet-How Many Squares (1)