GSEB Class 6 Maths Solutions Chapter 10 Mensuration InText Questions

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Question 1. Measure and write the length of the four sides of the top of your study table.
AB = 140 cm
BC = 80 cm
CD = 140 cm
DA = 80 cm
Now, the sum of the lengths of the four sides = AB + BC + CD + DA
= 140 cm + 80 cm + 140 cm + 80 cm = 440 cm
What is the perimeter of the page?
Answer:
Length of side AB = 140 cm
Length of side BC = 80 cm
Length of side CD = 140 cm
Length of side DA = 80 cm
The total sum of the lengths of the four sides is calculated as:
\( \text{Perimeter} = \text{AB} + \text{BC} + \text{CD} + \text{DA} \)
\( \text{Perimeter} = 140 \text{ cm} + 80 \text{ cm} + 140 \text{ cm} + 80 \text{ cm} \)
\( \text{Perimeter} = 440 \text{ cm} \)
Thus, the perimeter of the study table top is 440 cm. It is important to remember that these measurements will vary for different tables.
In simple words: First, measure each side of your table top. Then, add all these lengths together to find the total distance around the edge. This total distance is called the perimeter.

Exam Tip: Remember that perimeter is the total distance around the outside of a shape. Always ensure all side lengths are in the same unit before adding them up.

 

Question 2. Measure and write the lengths of the four sides of a page of your notebook. The sum of the lengths of the four sides = AB + BC + CD + DA = ____ cm + ____ cm + ____ cm + ____ cm = ____ cm. What is the perimeter of the page?
Answer: For a standard notebook page, you might find these approximate measurements:
Length (AB) = 29.7 cm
Width (BC) = 21 cm
Length (CD) = 29.7 cm
Width (DA) = 21 cm
The total sum of the lengths of the four sides is:
\( \text{Perimeter} = \text{AB} + \text{BC} + \text{CD} + \text{DA} \)
\( \text{Perimeter} = 29.7 \text{ cm} + 21 \text{ cm} + 29.7 \text{ cm} + 21 \text{ cm} \)
\( \text{Perimeter} = 101.4 \text{ cm} \)
Thus, the perimeter of the notebook page is 101.4 cm. Your own measurements might be slightly different.
In simple words: Take your notebook page and measure all four sides. Add these four measurements together to get the total perimeter. For example, if two sides are 29.7 cm and the other two are 21 cm, the total perimeter will be 101.4 cm.

Exam Tip: Always make sure to measure all sides accurately. For rectangular objects like notebook pages, opposite sides have equal lengths, which can simplify your measurements and calculations.

 

Question 3. Meera went to a park 150 m long and 80 m wide. She took one complete round on its boundary. What is the distance covered by her?
Answer:
The length of the park is 150 m.
The breadth (or width) of the park is 80 m.
To find the distance Meera covered in one complete round, we need to calculate the perimeter of the park.
The perimeter of a rectangular park is found by adding all its side lengths:
\( \text{Perimeter} = \text{Length} + \text{Breadth} + \text{Length} + \text{Breadth} \)
\( \text{Perimeter} = 150 \text{ m} + 80 \text{ m} + 150 \text{ m} + 80 \text{ m} \)
\( \text{Perimeter} = 460 \text{ m} \)
Therefore, the distance covered by Meera in taking one complete round of the park is 460 m.
In simple words: Meera walked all around the park. To find out how far she walked, you need to add up the lengths of all the sides of the park. Since the park is 150 meters long and 80 meters wide, adding these lengths (150 + 80 + 150 + 80) gives a total of 460 meters.

Exam Tip: For rectangular shapes, the perimeter can also be calculated using the formula \( 2 \times (\text{Length} + \text{Breadth}) \). Always include the correct units (e.g., meters, centimeters) in your final answer.

 

Question 4. Find the perimeter of the following figures:
(a) Perimeter = AB + BC + CD + DA = 40 cm + 10 cm + 40 cm + 10 cm = 100 cm
Answer:
(a) The figure is a rectangle with length 40 cm and width 10 cm. The perimeter is the sum of all its sides.
Given: AB = 40 cm, BC = 10 cm, CD = 40 cm, DA = 10 cm
\( \text{Perimeter} = \text{AB} + \text{BC} + \text{CD} + \text{DA} \)
\( \text{Perimeter} = 40 \text{ cm} + 10 \text{ cm} + 40 \text{ cm} + 10 \text{ cm} \)
\( \text{Perimeter} = 100 \text{ cm} \)
In simple words: For the first shape, we add the lengths of its four sides: 40 cm, 10 cm, 40 cm, and 10 cm. This gives a total perimeter of 100 cm.

Exam Tip: Always visually check the figure to identify if it's a regular shape (like a rectangle or square) to confirm which sides are equal, which can help in cross-checking your sum.

 

Question 4. Find the perimeter of the following figures:
(b) Perimeter = AB + BC + CD + DA = 5 cm + 5 cm + 5 cm + 5 cm = 20 cm
Answer:
(b) The figure is a square, where all sides are equal to 5 cm. The perimeter is the sum of all its sides.
Given: AB = 5 cm, BC = 5 cm, CD = 5 cm, DA = 5 cm
\( \text{Perimeter} = \text{AB} + \text{BC} + \text{CD} + \text{DA} \)
\( \text{Perimeter} = 5 \text{ cm} + 5 \text{ cm} + 5 \text{ cm} + 5 \text{ cm} \)
\( \text{Perimeter} = 20 \text{ cm} \)
In simple words: For the square shape, since all four sides are 5 cm long, we simply add 5 cm four times. This gives a total perimeter of 20 cm.

Exam Tip: For squares, a quick way to find the perimeter is to multiply the length of one side by 4. So, \( 4 \times \text{side} = \text{Perimeter} \).

 

Question 4. Find the perimeter of the following figures:
(c) Perimeter = AB + BC + CD + DE + EF + FG + GH + HI + IJ + JK + KL + LA = 1 cm + 3 cm + 3 cm + 1 cm + 3 cm + 3 cm + 1 cm + 3 cm + 3 cm + 1 cm + 3 cm + 3 cm = 28 cm
Answer:
(c) The figure is a polygon with many sides. To find the perimeter, we sum the lengths of all these individual sides.
Given side lengths: 1 cm, 3 cm, 3 cm, 1 cm, 3 cm, 3 cm, 1 cm, 3 cm, 3 cm, 1 cm, 3 cm, 3 cm.
\( \text{Perimeter} = 1+3+3+1+3+3+1+3+3+1+3+3 \)
\( \text{Perimeter} = 28 \text{ cm} \)
Thus, the perimeter of this complex figure is 28 cm.
In simple words: For shapes with many sides, like this one, you just need to measure each side and then add all those measurements together. When we add up all the given side lengths, we get a total perimeter of 28 cm.

Exam Tip: When dealing with complex polygons, it's helpful to tick off each side as you add its length to ensure you don't miss any or count any twice.

 

Question 4. Find the perimeter of the following figures:
(d) Perimeter=AB + BC + CD + DE + EF + FA = 100 m + 120 m + 90 m + 45 m + 60 m + 80 m = 495 m
Answer:
(d) The figure is a polygon with six distinct sides. To find the perimeter, we add up the lengths of all its sides.
Given side lengths: AB = 100 m, BC = 120 m, CD = 90 m, DE = 45 m, EF = 60 m, FA = 80 m.
\( \text{Perimeter} = \text{AB} + \text{BC} + \text{CD} + \text{DE} + \text{EF} + \text{FA} \)
\( \text{Perimeter} = 100 \text{ m} + 120 \text{ m} + 90 \text{ m} + 45 \text{ m} + 60 \text{ m} + 80 \text{ m} \)
\( \text{Perimeter} = 495 \text{ m} \)
Hence, the perimeter of this six-sided figure is 495 m.
In simple words: For this six-sided shape, we simply add the length of each side together: 100 m, 120 m, 90 m, 45 m, 60 m, and 80 m. The total sum of these lengths is 495 m, which is the perimeter.

Exam Tip: Always double-check your addition for longer sums. Writing down each number and adding them column by column can help prevent calculation errors.

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Question 1. Find the perimeter of the following rectangles:

Answer: The table above shows the calculations for the perimeter of each rectangle. We have filled in the missing values by applying both methods: summing all four sides and using the formula \( 2 \times (\text{Length} + \text{Breadth}) \). Both methods consistently yield the same perimeter for each rectangle, demonstrating their validity.
In simple words: To find the perimeter of a rectangle, you can either add the length of all four sides or use the quick formula: two times (length plus breadth). Both ways give you the same answer for how far it is around the edge of the rectangle.

Exam Tip: It is always useful to know both methods for calculating the perimeter of a rectangle, as they can help you check your work and ensure accuracy.

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Question 1. Find various objects from your surroundings that have regular shapes and find their perimeters.
Answer: This is an activity designed to help you explore geometry in your daily life. Here are some examples of objects you could find and measure:
1. **A Book:** Measure the length and width of a book cover. Calculate its perimeter using \( 2 \times (\text{Length} + \text{Width}) \).
2. **A Mobile Phone:** Measure its length and width. Calculate its perimeter.
3. **A Square Tile:** If you have square tiles on the floor or wall, measure one side. Its perimeter will be \( 4 \times \text{side length} \).
4. **A Photograph Frame:** Measure the outer edges of a rectangular frame to find its perimeter.
5. **A Window Pane:** Measure the length and breadth of a single pane of glass to determine its perimeter.
Remember to use a ruler or measuring tape and record your observations accurately.
In simple words: Look around your home or classroom for items shaped like squares or rectangles, such as books, phones, or tiles. Measure the edges of these things and then add them up to find the total distance around each item.

Exam Tip: When doing practical measurements, always note down the units (cm, inches) and ensure consistency in using the same unit throughout your calculations for each object.

 

Question 1. Draw any circle on a graph sheet. Count the squares and use them to estimate the area of the circular region.
Answer: This is an engaging activity to understand how area can be estimated for irregular or curved shapes. Here's how to do it:
1. **Draw a Circle:** Use a compass to draw a clear circle of any size on a graph sheet, ensuring its center aligns with a grid intersection for easier counting.
2. **Count Full Squares:** Count all the squares that are completely inside the circle.
3. **Count Half or More Squares:** Count all the squares that are more than half-filled by the circle.
4. **Ignore Less Than Half Squares:** Disregard any squares that are less than half-filled.
5. **Estimate Area:** Add the number of full squares and the number of more-than-half-filled squares. Multiply this total by the area of one small square (e.g., if each square is 1 cm by 1 cm, its area is 1 cm\(^2\)). This sum will provide an estimate of the circle's area. This method is an approximation, and more squares or smaller grid sizes generally offer better accuracy.
In simple words: Draw a circle on grid paper. Count all the squares that are fully inside the circle, and also those that are more than half inside. Add these counts together, and that sum will be your guess for the circle's area.

Exam Tip: For better accuracy, use a graph sheet with very small squares. The more squares you count that are almost full, the closer your estimate will be to the actual area.

 

Question 2. Trace shapes of leaves, flower petals, and other such objects on the graph paper and find their areas.
Answer: This activity teaches a practical method for estimating the area of irregularly shaped objects. Follow these steps:
1. **Select an Object:** Choose a leaf, flower petal, or another natural object with an interesting, non-standard shape.
2. **Trace:** Carefully place the object on a graph sheet and trace its outline using a pencil.
3. **Count Full Squares:** Count every complete square that falls entirely within the traced outline.
4. **Count Half-Filled Squares:** Count squares that are half or more covered by the outline. Treat each of these as one full square for estimation purposes.
5. **Calculate Area:** Sum the counts from steps 3 and 4. Multiply this total by the area of a single grid square (e.g., if each square is 1 cm\(^2\)), to get an estimated area of the object. This technique helps to approximate the space these natural shapes occupy.
In simple words: Pick a leaf or a flower, then draw its shape on grid paper. Count how many whole squares are inside your drawing. Also, count squares that are mostly inside. Add those numbers up, and you'll have an idea of the leaf's area.

Exam Tip: The more precise your tracing and counting, the better your area estimate will be. This method is particularly useful for shapes that do not fit standard area formulas.

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Question 1. Find the area on the floor of your classroom.
Answer: This is a practical activity to apply the concept of area to a large, real-world space. Here’s how you can perform it:
1. **Measure Length:** Use a measuring tape to find the length of your classroom floor from one end to the other. Record this measurement in meters.
2. **Measure Width:** Next, measure the width of the classroom floor from one side to the other. Record this in meters as well.
3. **Calculate Area:** Assuming your classroom floor is rectangular, its area can be calculated using the formula: Area = Length \( \times \) Width. Multiply the measured length by the measured width.
4. **Units:** Ensure your final answer is expressed in square meters (m\(^2\)). For example, if the length is 8 meters and the width is 6 meters, the area would be \( 8 \text{ m} \times 6 \text{ m} = 48 \text{ m}^2 \).
In simple words: To find the area of your classroom floor, measure how long it is and how wide it is. Then, multiply the length by the width. The answer will tell you how much space the floor covers.

Exam Tip: For large areas like a classroom floor, it's efficient to use meters for measurement. Always double-check your measurements to ensure accuracy in your final area calculation.

 

Question 2. Find the area of anyone's door in your house.
Answer: This activity allows you to calculate the area of a common household object. Here’s how you can do it:
1. **Measure Height:** Use a measuring tape to find the height of the door from top to bottom. Record this measurement in centimeters or meters.
2. **Measure Width:** Next, measure the width of the door from one side to the other. Record this in the same units as the height.
3. **Calculate Area:** A door is typically rectangular, so its area is calculated as: Area = Height \( \times \) Width. Multiply your measured height by your measured width.
4. **Units:** The area should be expressed in square centimeters (cm\(^2\)) or square meters (m\(^2\)), depending on the units you used for measuring. For instance, if a door is 200 cm high and 90 cm wide, its area would be \( 200 \text{ cm} \times 90 \text{ cm} = 18000 \text{ cm}^2 \).
In simple words: To figure out the area of a door, measure how tall it is and how wide it is. Then, just multiply those two numbers together. This product gives you the total space the door covers.

Exam Tip: Remember to use consistent units for both height and width before calculating the area. If one measurement is in centimeters and the other in meters, convert one of them so they are both the same.