RBSE Solutions Class 6 Maths Chapter 14 Perimeter and Area More Ques

Question 1. Find the perimeter of following rectangles. Which rectangle has the greatest perimeter?
(i)
(ii)
(iii)
(iv)
Answer:
(i) We find the perimeter of the rectangle by adding all its sides. Perimeter of rectangle = \( 2(l + b) = 2(2 + 3) = 2(5) = 10 \) cm.
(ii) We calculate the perimeter by adding all the side lengths. Perimeter of rectangle = \( 2(l + b) = 2(4 + 5) = 2(9) = 18 \) cm.
(iii) For this figure, the length and breadth are equal, making it a square. Perimeter of rectangle = \( 2(l + b) = 2(4 + 4) = 2(8) = 16 \) cm.
(iv) We add up all the side measurements to find the perimeter. Perimeter of rectangle = \( 2(l + b) = 2(7 + 2) = 2(9) = 18 \) cm.
The rectangles in (ii) and (iv) both have the greatest perimeter of 18 cm.
In simple words: To find the perimeter, you add up the lengths of all the sides of the shape. For a rectangle, you can also use the formula 2 times (length + breadth).

🎯 Exam Tip: Always remember that a square is a special type of rectangle where all four sides are equal, so its perimeter can also be found using the rectangle formula.

Question 1. Find the perimeter of a regular polygon with each side equal to 3.5 cm and number of sides equal to 3.
Answer: For a regular polygon, all sides are equal in length. To find the perimeter, we multiply the length of one side by the number of sides. In this case, each side is 3.5 cm long, and there are 3 sides. So, the perimeter is \( 3.5 \text{ cm} \times 3 = 10.5 \text{ cm} \). This polygon is actually an equilateral triangle.
In simple words: To get the perimeter of a regular shape, just multiply how long one side is by how many sides it has.

🎯 Exam Tip: Remember that a regular polygon has all sides and all angles equal. For a polygon with 3 sides, if all sides are equal, it's an equilateral triangle.

Question 2. Find the number of sides of a regular polygon if its perimeter is 28 cm and each side is 7 cm.
Answer: The perimeter of a regular polygon is found by multiplying the number of sides by the length of one side. Let 'n' be the number of sides. We are given that the perimeter is 28 cm and each side is 7 cm. So, we can write this as:
\( n \times 7 = 28 \)
\( \implies 7n = 28 \)
\( \implies n = \frac{28}{7} \)
\( \implies n = 4 \)
Therefore, the regular polygon has 4 sides. This means it is a square.
In simple words: If you know the total distance around a regular shape and the length of one side, you can find how many sides it has by dividing the total distance by the length of one side.

🎯 Exam Tip: Always state the type of polygon if the number of sides found corresponds to a common shape (e.g., 3 sides is a triangle, 4 sides is a square/quadrilateral).

Question 3. Find the perimeter of a square with each side equal to 4.5 cm.
Answer: A square has four equal sides. To find its perimeter, you can either add the length of all four sides or multiply the length of one side by 4. Each side of the square is 4.5 cm.
Total number of sides in a square = 4
Perimeter of square = \( 4 \times \text{side length} \)
Perimeter of square = \( 4 \times 4.5 \text{ cm} \)
Perimeter of square = \( 18.0 \text{ cm} \)
So, the perimeter of the square is 18 cm.
In simple words: To find the perimeter of a square, you just multiply the length of one side by four, because all its sides are the same length.

🎯 Exam Tip: Remember the specific properties of a square (all sides equal) to quickly calculate its perimeter or area. This is a basic but important concept.

Question 1. Put a leaf of a china rose plant and a leaf of a pepal tree on grid papers. Find the estimated areas of both. Compare and tell which leaf has greater area?
Answer: To find the estimated area of irregular shapes like leaves on grid paper, we count the squares covered by the leaf. We usually ignore squares that are less than half-filled and count squares that are half-filled or more than half-filled as one full square. After counting, we compare the total counts for each leaf.
(Refer to the solution for this question provided on page 197 of the textbook, where the areas are calculated by counting squares.)
In simple words: To compare the area of two leaves, you can place them on grid paper and count how many small squares each leaf covers. The leaf that covers more squares has a bigger area.

🎯 Exam Tip: When estimating area using grid paper, be consistent in how you count partially filled squares. A common method is counting full squares as 1, half-squares as 0.5, and ignoring squares less than half-filled.

Question 1. We measure perimeter and area only for closed figures. Think why?
Answer: We measure perimeter and area only for closed figures because these measurements define the boundary and space of a definite, complete shape. Perimeter is the total length around the outer boundary of a shape. If a figure is not closed, it doesn't have a clear, defined boundary all around it. Similarly, area is the amount of surface inside a boundary. An open figure has no enclosed space, so its area cannot be determined. These concepts require a fully enclosed region to be meaningful.
In simple words: We only measure the perimeter (distance around) and area (space inside) of shapes that are fully closed. This is because open shapes don't have a clear edge all the way around or a fixed space enclosed.

🎯 Exam Tip: Emphasize the definitions: perimeter as "distance around" and area as "space enclosed". These definitions inherently require a closed figure.

Question 2. Rashmi went to a park 120 m long and 80 m wide. She took one complete round on its boundary. What is the distance covered by her?
Answer: When Rashmi took one complete round on the boundary of the park, she covered a distance equal to the perimeter of the park. The park is rectangular with a length (l) of 120 m and a breadth (b) of 80 m.
The formula for the perimeter of a rectangle is \( 2 \times (l + b) \).
Distance covered = Perimeter of park
Distance covered = \( 2 \times (120 \text{ m} + 80 \text{ m}) \)
Distance covered = \( 2 \times (200 \text{ m}) \)
Distance covered = \( 400 \text{ m} \)
So, Rashmi covered a total distance of 400 m.
In simple words: Going one full circle around a park means walking its whole perimeter. For a rectangle, you add the length and width, then multiply by two to find this total distance.

🎯 Exam Tip: Identify keywords like "complete round" or "boundary" to understand that the question is asking for the perimeter, not the area, of the shape.

Question 3. Following figure is a closed figure made of various line segments. Find the perimeter of the figure by adding the lengths of the line segments.
Answer: To find the perimeter of a figure made of several line segments, we need to add the lengths of all the individual segments that form its outer boundary. In this figure, all segments have a length of 2 cm.
Perimeter = AB + BC + CD + DE + EF + FG + GH + HI + IJ + JK + KL + LA
Perimeter = \( 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 \) cm
Since there are 12 segments, each 2 cm long, the total perimeter is:
Perimeter = \( 12 \times 2 \text{ cm} \)
Perimeter = \( 24 \text{ cm} \)
Thus, the perimeter of the figure is 24 cm.
In simple words: When a shape is made of many straight lines, you find its perimeter by adding up the length of every single one of those lines on the outside.

🎯 Exam Tip: For irregular polygons, ensure you count every single side and add its length. Be careful not to miss any segment or double-count one. Clearly label points to keep track of segments.

Question 4. Find the perimeter of the following figure.
Answer: The perimeter of any polygon is the sum of the lengths of all its sides. Assuming the figure has sides PQ, QR, RS, ST, TU, and UP with the given lengths:
Perimeter = PQ + QR + RS + ST + TU + UP
Perimeter = \( 80 + 120 + 140 + 60 + 100 + 50 \) m
Perimeter = \( 550 \) m
So, the perimeter of the figure is 550 m. This shape could be a hexagon if all these segments form its boundary.
In simple words: Just add up the lengths of all the outside lines of the shape to find its perimeter.

🎯 Exam Tip: Always make sure to include every side of the polygon in your sum. It's helpful to tick off each side as you add it to avoid missing any.

Question 1. Find the perimeter of the following rectangles. Which rectangle has the greatest perimeter?
(i)
(ii)
(iii)
(iv)
Answer: To find the perimeter of each rectangle, we use the formula \( 2 \times (\text{length} + \text{breadth}) \). Then, we compare the perimeters to see which is the largest.
(i) On measuring, length (l) = 1.8 cm and breadth (b) = 1.3 cm.
Perimeter = \( 2 \times (1.8 + 1.3) = 2 \times (3.1) = 6.2 \) cm.
(ii) On measuring, length (l) = 1.5 cm and breadth (b) = 0.8 cm.
Perimeter = \( 2 \times (1.5 + 0.8) = 2 \times (2.3) = 4.6 \) cm.
(iii) On measuring, length (l) = 2.1 cm and breadth (b) = 1.6 cm.
Perimeter = \( 2 \times (2.1 + 1.6) = 2 \times (3.7) = 7.4 \) cm.
(iv) On measuring, length (l) = 1.8 cm and breadth (b) = 1.2 cm.
Perimeter = \( 2 \times (1.8 + 1.2) = 2 \times (3.0) = 6.0 \) cm.
Comparing all perimeters: 6.2 cm, 4.6 cm, 7.4 cm, 6.0 cm.
The rectangle in (iii) has the greatest perimeter of 7.4 cm.
In simple words: Calculate the perimeter for each rectangle by adding up its two lengths and two breadths. Then, look at all the answers to see which number is the biggest.

🎯 Exam Tip: When comparing multiple figures, calculate each value accurately before making a comparison. Double-check your addition and multiplication for each perimeter.

Question 1. Madhav and Ishaan are making different polygons with the help of similar straws. Following are a few of the shapes they made. Measure of lengths of the sides of these figures and fill in the table.
Answer: To understand the perimeter of polygons, we measure the length of each side and then calculate the total sum. The table shows the details for different polygons made by Madhav and Ishaan, based on their side measurements.

In simple words: The table shows that for regular polygons (where all sides are equal), you can find the total length around the shape by either adding all the side lengths or by multiplying the length of one side by the number of sides. Both methods give the same answer.

🎯 Exam Tip: When dealing with regular polygons, both summing all side lengths and multiplying (number of sides × length of one side) are valid methods for calculating perimeter. Choose the one that is most efficient for the given problem.

Question 1. The closed figures given below occupy some space on a flat surface. Can you tell which figure occupies more space?
Answer: To find out which figure occupies more space, we need to compare their areas. Simply looking at them can give a general idea, but for a precise comparison, especially if the sizes are similar, we need a method to measure their area. The table below shows the area occupied by different figures.

In simple words: To know which shape takes up more room, you compare their areas. Sometimes you can tell by just looking, especially if one is much bigger, but for a clear answer, you need to measure the area properly.

🎯 Exam Tip: Visual estimation is often unreliable for closely sized figures. Always rely on calculation or systematic measurement (like counting squares on a grid) for accurate area comparison.

Question 1. Can you tell which of the following figures has larger area, just by looking them?
Answer: It is usually difficult to tell which figure has a larger area just by looking at irregular shapes like leaves. To accurately compare their areas, we need to use a method such as placing them on grid paper and counting the squares they cover.
For the china rose leaf and pepal leaf:
We count the squares covered by each leaf. We consider fully-filled squares and more than half-filled squares as one square unit, and ignore less than half-filled squares.
Area of china rose leaf = 25 square units
Area of pepal leaf = 15 square units
To compare, we can find the ratio:
Ratio of Area of china rose leaf to pepal leaf = \( 25 : 15 = 5 : 3 \)
Since 25 > 15, the china rose leaf has a greater area.
In simple words: You can't always tell which leaf is bigger just by looking. You have to put each leaf on a grid of squares and count how many squares it covers. The leaf that covers more squares has a bigger area.

🎯 Exam Tip: When working with irregular shapes on grid paper, be consistent in your method of counting squares. Clearly define what counts as a full square (e.g., more than half-filled) and what does not.

Question 1. Place three rectangle A, B and C squared grid paper or graph paper where every square measures 1 cm × 1 cm. Look at the figure and fill in the following table.
Answer: We can find the area of a rectangle by multiplying its length and breadth. The number of squares enclosed by a rectangle also gives its area, assuming each square is 1 cm by 1 cm. Let's fill the table based on the given figures.

In simple words: The number of squares inside a rectangle is the same as its area. You can find this by multiplying the length by the breadth. Each square is like one unit of area.

🎯 Exam Tip: This exercise visually confirms that the area of a rectangle (Length x Breadth) directly corresponds to the count of 1x1 unit squares it contains. Always use consistent units for length and breadth to get the area in square units.

Question 1. Take a grid paper with every square measures 1 cm x 1 cm. Take 22 pieces of thin string's each 1 cm long. Place these strings on the gird paper and make different rectangles each with perimeter equal to 22 cm. Fill the detail in the given table. For each figure, count the number of squares. What do you infer from table?
Answer: We use 22 cm of string to form rectangles, meaning the perimeter of each rectangle must be 22 cm. We then measure their lengths and breadths and calculate their areas by counting the 1 cm x 1 cm squares they enclose.

Conclusion: From the table, we infer that as the length of the rectangle increased, its breadth decreased, which also caused the area of the rectangle to decrease. This shows that for a fixed perimeter, different dimensions can result in different areas.
In simple words: If you keep the total distance around a rectangle (its perimeter) the same, you can make different shapes. As one side gets longer, the other side gets shorter, and the total space inside (the area) can also change.

🎯 Exam Tip: Understand that figures with the same perimeter can have different areas. Often, a shape that is closer to a square will have a larger area for a given perimeter compared to a very long, thin rectangle.

Question 1. Make as many rectangles as you can, such that enclosed area of each rectangle is 24 squares. Fill the detail about their length and breadth in a table. What do you infer from the table?
Answer: We need to find different pairs of lengths and breadths that multiply to give an area of 24 square units (if 1 square = 1 sq. cm, then 24 sq. cm).
Possible measurements for length and breadth that give an area of 24 sq. cm are:
1 cm and 24 cm;
2 cm and 12 cm;
3 cm and 8 cm;
4 cm and 6 cm.

Conclusion: The table shows that when the area remains the same, if the length decreases, the breadth increases. The product of length and breadth (which is the area) stays constant in all these cases.
In simple words: For a fixed area, you can have different shapes of rectangles. If one side gets shorter, the other side must get longer to keep the total enclosed space the same.

🎯 Exam Tip: This exercise demonstrates that many pairs of factors can result in the same product (area). Understanding factor pairs is key to finding all possible dimensions for a given area.

Question 2. Given below are figures of the plots of Poonam and Pooja. Whose plot has greater area?
Answer: To find out whose plot has a greater area, we need to calculate the area of each plot and then compare them.
Poonam's plot is a square with side length 50 m.
Area of Poonam's plot = side \( \times \) side = \( 50 \text{ m} \times 50 \text{ m} = 2500 \) sq. m.
Pooja's plot is a rectangle with length 70 m and breadth 30 m.
Area of Pooja's plot = length \( \times \) breadth = \( 70 \text{ m} \times 30 \text{ m} = 2100 \) sq. m.
Comparing the areas:
\( 2500 \text{ sq. m} > 2100 \text{ sq. m} \)
Therefore, Poonam's plot has a greater area.
In simple words: We calculate the space inside each plot. Poonam's plot covers 2500 square meters, and Pooja's covers 2100 square meters. Since 2500 is bigger than 2100, Poonam's plot is larger.

🎯 Exam Tip: Carefully identify the shape of each plot (square, rectangle) before applying the correct area formula. Pay attention to the units (meters, square meters) in your answer.

Question 1. A piece of square cloth 80 cm wide. What will be the change in the perimeter of the cloth if:
(i) There will be no change in perimeter if we cut handkerchief like this figure, because after cutting the handkerchief two sides less and two new sides forms of same size. i.e. equal sides removed and formed.
(ii) New perimeter in this figure is as below
Perimeter = 80 + 80 + 80 + 30 + 20 + 20 + 20 + 30 = 240 + 120 = 360 cm
In this case, perimeter (RBSESolutions.com) increased, because after cutting the handkerchief, one side of 20 cm less from a side and three new sides of 20 cm each forms their.
Answer: Initially, the cloth is a square, 80 cm wide. So, its length and breadth are both 80 cm.
Perimeter of the initial square cloth = \( 2 \times (\text{length} + \text{breadth}) = 2 \times (80 + 80) = 2 \times (160) = 320 \) cm.
(i) If a portion is cut out in a way that the removed length is replaced by new lengths of the same total measure, the perimeter remains unchanged. For example, if a corner is cut out as a smaller square, but the cuts follow the original square's lines, the perimeter stays the same. The two sides removed are replaced by two new sides of the same length, maintaining the total perimeter.
(ii) In the second figure, when the handkerchief is cut, the perimeter changes. We need to sum the lengths of all the new outer edges.
New Perimeter = \( 80 + 80 + 80 + 30 + 20 + 20 + 20 + 30 \) cm
New Perimeter = \( 240 + 120 \) cm
New Perimeter = \( 360 \) cm.
In this case, the perimeter increased from 320 cm to 360 cm. This happens because one original side (80 cm) is replaced by shorter segments that add up to a greater total length, for example, an 80 cm side might be replaced by a 30 cm, 20 cm, 20 cm, and 30 cm sequence, which sums to 100 cm. The cut removed 20 cm from one side, but added three new 20 cm sides, effectively adding to the total perimeter.
In simple words: When you cut a shape, the perimeter can change. If the cuts just push the boundary inwards without adding new length, the perimeter might stay the same. But if the cuts create new, longer paths along the edge, the perimeter will get bigger.

🎯 Exam Tip: When a figure is cut, visualize how the new perimeter is formed. Segments that were internal to the cut region can become part of the new external perimeter, and some original external segments might be removed. Sum all new external edges carefully.