Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 1 Geometry InText Questions

Activity 1 (Text Book Page No. 2)

Write the perimeter of each figure:

Question 1.
Answer: For this rectangular shape, we add the lengths of all its sides. The lengths are 5 cm, 6 cm, 5 cm, and 6 cm. Adding them up, we get \( 5 + 6 + 5 + 6 = 22 \) cm. This gives the total distance around the figure.
In simple words: Add up all the side lengths of the figure to find its perimeter.

🎯 Exam Tip: When finding the perimeter of a rectangle, ensure you add both the length and the width twice, or use the formula \( 2 \times ( \text{length} + \text{width} ) \).

Question 2.
Answer: This figure is a square, which means all four of its sides are equal in length. Each side measures 4 cm. To find the perimeter, we add all four side lengths: \( 4 + 4 + 4 + 4 = 16 \) cm. Therefore, the total boundary length is 16 cm.
In simple words: For a square, just add the length of one side four times to get the perimeter.

🎯 Exam Tip: Remember that all sides of a square are equal, which simplifies perimeter calculation to \( 4 \times \text{side} \).

Question 3.
Answer: This figure is a triangle, which has three sides. To find its perimeter, we add the lengths of these three sides. The side lengths are 3 cm, 5 cm, and 7 cm. Adding them together, we get \( 3 + 5 + 7 = 15 \) cm. This is the total distance around the triangle.
In simple words: For a triangle, add the lengths of its three edges together to find the perimeter.

🎯 Exam Tip: Always check that you have added all sides, especially for shapes with many sides, to get the correct perimeter.

Question 4.
Answer: To find the perimeter of this irregular shape, we need to add the lengths of all its outer sides. The lengths are 6 cm, 3 cm, 4 cm, 3 cm, 4 cm, 3 cm, 6 cm, and 9 cm. Adding all these values: \( 6 + 3 + 4 + 3 + 4 + 3 + 6 + 9 = 38 \) cm. This sum represents the entire boundary of the figure.
In simple words: Just add the length of every single outside edge of the shape to get its total perimeter.

🎯 Exam Tip: For complex shapes, carefully trace the outline and list each side length to avoid missing any part of the perimeter calculation.

Question 5.
Answer: This figure is a hexagon-like shape with six sides. To find its perimeter, we add the lengths of all six sides. The lengths are 5 cm, 5 cm, 10 cm, 5 cm, 5 cm, and 10 cm. Adding them up, we get \( 5 + 5 + 10 + 5 + 5 + 10 = 40 \) cm. So, the total distance around the shape is 40 cm.
In simple words: Find the perimeter by adding the lengths of all six sides of this hexagon-like shape.

🎯 Exam Tip: Always count the number of sides in a polygon to ensure all measurements are included in the perimeter calculation.

Question 6.
Answer: For this five-sided shape, we calculate the perimeter by adding the lengths of all its sides. The lengths shown are 11 cm, 16 cm, 7 cm, 7 cm, and 16 cm. Adding these values: \( 11 + 16 + 7 + 7 + 16 = 57 \) cm. Each side contributes to the total distance around the figure.
In simple words: Add all five side lengths of the figure together to find its perimeter.

🎯 Exam Tip: Carefully identify and sum all exterior edge lengths, ensuring no side is missed or counted twice, especially for irregular polygons.

Try This (Text Book Page No. 5)

Question. If a square of side 1 cm is cut out of the corner of a larger square with side 4 cm (See the figure). What will be the perimeter of the remaining shape?
Answer: First, the original large square has sides of 4 cm, so its perimeter would be \( 4 \times 4 = 16 \) cm.
When a 1 cm square is cut from a corner, two outer sides of 1 cm each are removed. However, two new inner sides, also 1 cm each, are created. This means the total length around the shape remains unchanged.
The perimeter of the remaining shape is calculated as: \( 4 \text{cm} + 4 \text{cm} + (4-1) \text{cm} + 1 \text{cm} + 1 \text{cm} + (4-1) \text{cm} \).
So, it becomes \( 4 \text{cm} + 4 \text{cm} + 3 \text{cm} + 1 \text{cm} + 1 \text{cm} + 3 \text{cm} = 16 \text{cm} \).
Therefore, the perimeter of the remaining shape is 16 cm.
In simple words: Even after cutting a small square from the corner, the distance around the shape stays the same as the original big square. The two cut edges are replaced by two new inner edges of the same length.

🎯 Exam Tip: When a corner square is removed, the perimeter often remains unchanged because the removed outer edges are replaced by new inner edges of equal total length.

Activity 2 (Text Book Page No. 10)

Using the grid sheet find the area and perimeter of the rectangles and squares. Each square is 1 sq. cm.

Question. Find the area of the 2x2 square.
Answer: For the first figure, a 2x2 square, we count the number of small squares inside it. There are 2 rows with 2 squares in each row, making a total of \( 2 \times 2 = 4 \) squares. Since each square is 1 sq. cm, the area is 4 sq. cm.
In simple words: Just count all the little squares inside the big shape. That number is its area.

🎯 Exam Tip: Area is the space inside a two-dimensional shape, often measured by counting the unit squares that cover it.

Question. Find the area of the 2x5 rectangle.
Answer: For the second figure, a rectangle with 2 rows and 5 columns, we count the total number of small squares. This is calculated as \( 2 \times 5 = 10 \) squares. As each square is 1 sq. cm, the area of this rectangle is 10 sq. cm.
In simple words: Count the rows and columns, then multiply them to find how many squares are inside.

🎯 Exam Tip: To find the area of a rectangle on a grid, count the number of unit squares along its length and width, then multiply these numbers.

Question. Find the area of the 3x3 square.
Answer: For the third figure, a 3x3 square, we count the small squares. There are 3 rows and 3 columns, which gives \( 3 \times 3 = 9 \) squares. Since each square is 1 sq. cm, the area of this square is 9 sq. cm.
In simple words: For a square, multiply its side length by itself to get its area.

🎯 Exam Tip: Always state units (like 'sq. cm') clearly when giving the area to indicate the measurement type.

Question. Find the area of the 3x5 rectangle.
Answer: For the fourth figure, a 3x5 rectangle, we count the small squares within its boundary. There are 3 rows and 5 columns, resulting in \( 3 \times 5 = 15 \) squares. Since each square covers 1 sq. cm, the total area of the rectangle is 15 sq. cm.
In simple words: The total area is found by counting all the small square units that make up the shape.

🎯 Exam Tip: Practice counting squares on a grid to quickly determine the area of various shapes and improve your spatial reasoning skills.