Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 1 Geometry Exercise 1.2

Tamilnadu Samacheer Kalvi 5th Maths Solutions Term 3 Chapter 1 Geometry Ex 1.2

Question 1. The length of the side of each square is given below. Find its area.
(i) 10 metres
(ii) 5 cm
(iii) 15 metres
(iv) 16 cm
Answer:
(i) Side = 10 metres
Area of the square \( = \text{Length of a side} \times \text{Length of a side} \)
\( = 10 \times 10 = 100 \text{ sq.m} \)
(ii) Side = 5 cm
Area of the square \( = \text{Length of a side} \times \text{Length of a side} \)
\( = 5 \times 5 = 25 \text{ sq.cm} \)
(iii) Side = 15 metres
Area of the square \( = \text{Length of a side} \times \text{Length of a side} \)
\( = 15 \times 15 = 225 \text{ sq.m} \)
(iv) Side = 16 cm
Area of the square \( = \text{Length of a side} \times \text{Length of a side} \)
\( = 16 \times 16 = 256 \text{ sq.cm} \)
In simple words: To find the area of a square, you just multiply the length of one side by itself. Make sure to use the correct unit like square metres or square centimetres.

🎯 Exam Tip: Always remember that the unit for area is always "square units," such as sq.m or cm\(^2\), matching the unit of length given.

Question 2. Find the area of the following rectangles.
(i) length = 6 cm and breadth = 3 cm
(ii) length = 7 in and breadth = 4
(iii) length = 8 cm and breadth = 5 cm
(iv) length = 9 m and breadth = 6 m
Answer:
(i) Length = 6 cm and Breadth = 3 cm
Area of the rectangle \( = \text{Length} \times \text{Breadth} \)
\( = 6 \text{ cm} \times 3 \text{ cm} = 18 \text{ cm}^2 \)
(ii) Length = 7 in and Breadth = 4 in (assuming consistent units)
Area of the rectangle \( = \text{Length} \times \text{Breadth} \)
\( = 7 \text{ cm} \times 4 \text{ cm} = 28 \text{ cm}^2 \)
(iii) Length = 8 cm and Breadth = 5 cm
Area of the rectangle \( = \text{Length} \times \text{Breadth} \)
\( = 8 \text{ cm} \times 5 \text{ cm} = 40 \text{ cm}^2 \)
(iv) Length = 9 m and Breadth = 6 m
Area of the rectangle \( = \text{Length} \times \text{Breadth} \)
\( = 9 \text{ m} \times 6 \text{ m} = 54 \text{ m}^2 \)
In simple words: To find the area of a rectangle, you multiply its length by its breadth. Always make sure the units for length and breadth are the same before multiplying.

🎯 Exam Tip: Pay close attention to the units provided (cm, m, in) and ensure your answer's area unit matches them correctly (cm\(^2\), m\(^2\), in\(^2\)).

Question 3. If the cost of 1 sq.m of a plot is Rs 800, then find the total cost of the plot that is 15 m long and 10 m breadth.
Answer:
Length of the plot = 15 m
Breadth of the plot = 10 m
Area of the plot \( = \text{Length} \times \text{Breadth} \)
\( = 15 \text{ m} \times 10 \text{ m} = 150 \text{ sq.m} \)
Cost of 1 sq.m of land = Rs 800
Total cost of the plot \( = \text{Area of the plot} \times \text{Cost per sq.m} \)
\( = 150 \times 800 = 1,20,000 \text{ rupees} \)
In simple words: First, calculate the total area of the plot by multiplying its length and breadth. Then, multiply this total area by the cost of one square metre to find the full cost of the plot.

🎯 Exam Tip: When calculating costs involving area, always ensure the units for area and the cost per unit area match perfectly to avoid errors.

Question 4. The side of a square is 6 cm. The length of a rectangle is 10 cm and its breadth is 4 cm. Find the perimeter and area of both the square and rectangle.
Answer:
**For the Square:**
Side of the square = 6 cm
Perimeter of a square \( = 4 \times \text{length of a side} \)
\( = 4 \times 6 \text{ cm} = 24 \text{ cm} \)
Area of a square \( = \text{length of a side} \times \text{length of a side} \)
\( = 6 \times 6 = 36 \text{ cm}^2 \)

**For the Rectangle:**
Length of the rectangle = 10 cm
Breadth of the rectangle = 4 cm
Perimeter of a rectangle \( = 2 \times \text{length} + 2 \times \text{breadth} \)
\( = 2 \times 10 + 2 \times 4 \)
\( = 20 + 8 = 28 \text{ cm} \)
Area of a rectangle \( = \text{length} \times \text{breadth} \)
\( = 10 \times 4 = 40 \text{ cm}^2 \)
In simple words: For a square, perimeter is four times its side, and area is side multiplied by side. For a rectangle, perimeter is two times (length plus breadth), and area is length multiplied by breadth.

🎯 Exam Tip: Remember the specific formulas for perimeter and area for both squares and rectangles to apply them correctly based on the given dimensions.

Question 5. What will be the labour cost of laying the floor of an assembly hall which is 14 m long and 10 m breadth if the cost of laying is 60 per sq.m?
Answer:
Length of the assembly hall = 14 m
Breadth of the assembly hall = 10 m
Area of the assembly hall \( = \text{length} \times \text{breadth} \)
\( = 14 \text{ m} \times 10 \text{ m} = 140 \text{ sq.m} \)
Cost of laying 1 sq.m = Rs 60
Total cost of laying the floor \( = \text{Total Area} \times \text{Cost per sq.m} \)
\( = 140 \times 60 = 8400 \text{ rupees} \)
In simple words: First, calculate the total area of the floor by multiplying its length and breadth. Then, multiply this area by the cost given for each square metre to find the total labour cost.

🎯 Exam Tip: Always make sure the units in the question (e.g., metres for length, sq.m for cost) are consistent throughout your calculations to get the correct final answer.