CBSE Class 5 Mathematics How Many Squares Worksheet Set 04

Competency - Understanding Basic Concepts

Question 1. Here is a rectangle of area 8 sq.cm. a) Draw 2 straight lines in this rectangle to divide it into 1 rectangle and 2 equal triangles. Find the area of the new rectangle and the area of 1 of the triangles.
Answer: 1. Observe the given rectangle of area \(8 \text{ sq.cm}\) drawn on the grid, which consists of \(8\) unit squares (each of side \(1\text{ cm}\) and area \(1 \text{ sq.cm}\)).
2. The dimensions of the given rectangle are length \(4\text{ cm}\) and breadth \(2\text{ cm}\).
3. Draw two diagonal lines from opposite corners or split the grid such that one middle section forms a smaller rectangle and the remaining parts form two equal right-angled triangles.
4. For example, if the new rectangle is formed by \(4\) unit squares in the middle or side, its area is \(4 \text{ sq.cm}\).
5. The remaining area of \(8 - 4 = 4 \text{ sq.cm}\) is divided into \(2\) equal triangles.
6. Area of 1 triangle = \(\frac{4}{2} = 2 \text{ sq.cm}\).
In simple words: We split the original shape into a smaller rectangle and two identical triangles, then calculated their areas based on the unit squares.

Exam Tip: Remember that the area of a right-angled triangle is half the area of the rectangle or square it is formed from: \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\).

Question 2. Rearrange the squares in the rectangle to form another rectangle whose perimeter is 18cm.
Answer: 1. The original rectangle has an area of \(8 \text{ sq.cm}\), which means it is made up of \(8\) unit squares of side \(1\text{ cm}\).
2. To form a new rectangle using all \(8\) unit squares, the product of its length and breadth must be \(8\) (\(\text{Length} \times \text{Breadth} = 8\)).
3. The possible whole number dimensions for a rectangle of area \(8 \text{ sq.cm}\) are: - \(8\text{ cm} \times 1\text{ cm}\) - \(4\text{ cm} \times 2\text{ cm}\)
4. Let us test the perimeter for both sets of dimensions using the formula \(\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})\): - For \(8\text{ cm} \times 1\text{ cm}\): Perimeter = \(2 \times (8 + 1) = 2 \times 9 = 18\text{ cm}\). - For \(4\text{ cm} \times 2\text{ cm}\): Perimeter = \(2 \times (4 + 2) = 2 \times 6 = 12\text{ cm}\).
5. Therefore, the required rectangle must have dimensions \(8\text{ cm}\) by \(1\text{ cm}\) so that its perimeter is exactly \(18\text{ cm}\).
In simple words: We rearranged the 8 unit squares into a long strip of 8 units by 1 unit, which gives a perimeter of 18 cm.
Exam Tip: Always test all possible factor pairs of the area when looking for a specific perimeter

Please refer to attached file for CBSE Class 5 Maths Worksheet-How Many Squares (4)