Maharashtra Board Class 5 Maths Chapter 12 Perimeter and Area Set 49 Solutions

Std 5 Maths Chapter 12 Perimeter And Area

Question 1. How much wire will be needed to make a rectangle 7 cm long and 4 cm wide?
Answer: Perimeter of a rectangle
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 7 + 2 \times 4 \)
= \( 14 + 8 \)
= \( 22 \text{ cm} \)
Therefore, 22 cm wire will be needed to make a rectangle.
In simple words: To find the wire needed for a rectangle, calculate its perimeter by adding up all its side lengths. For a rectangle with a length of 7 cm and a width of 4 cm, the total wire needed is 22 cm.

🎯 Exam Tip: Remember the formula for the perimeter of a rectangle: 2(length + breadth). Show all calculation steps clearly to score full marks.

Question 2. If the length of a rectangle is 20 m and its width is 12m, what is its perimeter?
Answer: Perimeter of a rectangle
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 20 + 2 \times 12 \)
= \( 40 + 24 \)
= \( 64 \text{ m} \)
Therefore, the perimeter is 64 m.
In simple words: The perimeter of a rectangle is found by adding twice its length and twice its width. For a rectangle 20 m long and 12 m wide, the perimeter is 64 m.

🎯 Exam Tip: Always include the correct unit (like 'm' for meters or 'cm' for centimeters) in your final answer for perimeter calculations.

Question 3. Each side of a square is 9 m long. Find its perimeter.
Answer: Perimeter of a square
= \( 4 \times \text{length of one side} \)
= \( 4 \times 9 \)
= \( 36 \text{ m} \)
Therefore, the perimeter is 36 m.
In simple words: To find the perimeter of a square, multiply the length of one side by 4. If each side is 9 m, the perimeter is 36 m.

🎯 Exam Tip: Distinguish between perimeter formulas for squares (4 x side) and rectangles (2 x length + 2 x breadth) to avoid common errors.

Question 4. If we take 4 rounds around a field that is 160 m long and 90 m wide, what is the distance we walk in kilometres?
Answer: Perimeter of a rectangular field
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 160 + 2 \times 90 \)
= \( 320 + 180 \)
= \( 500 \text{ m} \)
In one round, the distance walked is 500 m.
Hence, distance walked in 4 rounds
= \( 500 \times 4 \)
= \( 2000 \text{ m} \)
= \( 2 \text{ km} \)
Therefore, the distance walked in 4 rounds is 2 km.
In simple words: First, calculate the perimeter of the field (one round). Then, multiply that by the number of rounds (4) to get the total distance. Finally, convert meters to kilometers. For a field 160m long and 90m wide, 4 rounds equal 2 km.

🎯 Exam Tip: Pay close attention to unit conversions (e.g., meters to kilometers) as they are often a source of mistakes in multi-step problems.

Question 5. Sanju completes 12 rounds around a square park every day. If one side of the park is 120 m, find out in kilometres and metres the distance that Sanju covers daily.
Answer: Perimeter of a square
= \( 4 \times \text{length of one side} \)
= \( 4 \times 120 \)
= \( 480 \text{ m} \)
So, in one round the distance covered is 480 m.
Hence, in 12 rounds the distance covered is
= \( 480 \times 12 \)
= \( 5760 \text{ m} \)
= \( 5000 \text{ m} + 760 \text{ m} \)
= \( 5 \text{ km } 760 \text{ m} \)
Therefore, Sanju covers 5 km 760 m daily.
In simple words: Calculate the perimeter of the square park (one round). Then, multiply this by the number of rounds (12) to find the total distance in meters, and convert it into kilometers and meters. Sanju covers 5 km 760 m daily.

🎯 Exam Tip: When converting meters to kilometers and meters, remember that 1000 meters equals 1 kilometer. Clearly show both the total meters and the final km/m conversion.

Question 6. The length of a rectangular plot of land is 50 m and its width is 30 m. A triple fence has to be put along its edges. If the wire costs 60 Rs. permetre, what will be the total cost of the wire needed for the fence?
Answer: Perimeter of a rectangular plot
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 50 + 2 \times 30 \)
= \( 100 + 60 \)
= \( 160 \text{ m} \)
For a triple fence, wire needed
= \( 3 \times 160 \)
= \( 480 \text{ m} \)
Cost of the wire needed
= \( \text{wire needed} \times \text{rate} \)
= \( 480 \times 60 \)
= \( 28800 \text{ Rs.} \)
Therefore, the total cost of the wire needed for the fence is Rs. 28,800.
In simple words: First, find the perimeter of the plot for one fence. Since it's a triple fence, multiply the perimeter by 3 to get the total wire length. Finally, multiply the total wire length by the cost per meter to find the total cost.

🎯 Exam Tip: Break down complex problems into smaller, manageable steps (perimeter, total wire, total cost). Always double-check calculations involving multiplication and currency.

Question 7. A game requires its players to run around a square playground. Each side of the playground is 20 m long. One player took 5 rounds around the playground. How many metres did he run altogether?
Answer: Perimeter of a square
= \( 4 \times \text{length of one side} \)
= \( 4 \times 20 \)
= \( 80 \text{ m} \)
In one round, the distance is 80 m.
So in 5 rounds, the distance is
= \( 80 \times 5 \)
= \( 400 \text{ m} \)
Therefore, he runs altogether = 400 m.
In simple words: Calculate the perimeter of the square playground to find the distance of one round. Then multiply this by the number of rounds (5) to find the total distance run.

🎯 Exam Tip: For problems involving multiple rounds, first calculate the perimeter for a single round, then multiply by the number of rounds. Ensure the final unit matches the question's requirement (here, meters).

Question 8. Four rounds of wire fence have to be put around a field. If the field is 60 m long and 40 m wide, how much wire will be needed?
Answer: Perimeter of rectangular field
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 60 + 2 \times 40 \)
= \( 120 + 80 \)
= \( 200 \text{ m} \)
Hence, wire required for 4 rounds
= \( 200 \times 4 \)
= \( 800 \text{ m} \)
Therefore, wire required for 4 rounds = 800 m.
In simple words: First, calculate the perimeter of the rectangular field for one layer of fence. Then, multiply this perimeter by 4 to find the total length of wire needed for four rounds.

🎯 Exam Tip: Clearly state the perimeter of one round before calculating for multiple rounds. Always check if the question asks for a single perimeter or a total for multiple repetitions.

Question 9. The sides of a triangle are 24.7cm, 20.4 cm and 10.5 cm respectively. What is the perimeter of the triangle?
Answer: Perimeter of triangle
= \( 24.7 + 20.4 + 10.5 \)
= \( 55.6 \text{ cm} \)
Therefore, the perimeter of a triangle = 55.6 cm.
In simple words: The perimeter of any triangle is the sum of the lengths of its three sides. Adding the given side lengths (24.7 cm, 20.4 cm, and 10.5 cm) gives a total perimeter of 55.6 cm.

🎯 Exam Tip: For triangles, perimeter is simply the sum of all three sides. Ensure accurate addition, especially with decimal numbers, and always include units.

Question 10. Look at the figures on the sheet of graph paper. Measure their sides with the help of the lines on the graph paper. Write the perimeter of each in the right box.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र ग्राफ पेपर पर विभिन्न आकृतियों जैसे आयत ABCD, आयत EFGH, वर्ग PQRS, आयत STUV और त्रिभुज LMN को दर्शाता है। छात्रों को इन आकृतियों की भुजाओं को ग्राफ पेपर की रेखाओं की मदद से मापना है ताकि उनका परिमाप ज्ञात किया जा सके और दिए गए खाली स्थानों में भरना है।
Answer:
(1) Perimeter of a rectangle ABCD
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 3.5 + 2 \times 2.5 \)
= \( 7 + 5 \)
= \( 12 \text{ cm} \)
(2) Perimeter of a rectangle EFGH
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 3.8 + 2 \times 1.3 \)
= \( 7.6 + 2.6 \)
= \( 10.2 \text{ cm} \)
(3) Perimeter of a rectangle PQRS
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 2.4 + 2 \times 2.4 \)
= \( 4.8 + 4.8 \)
= \( 9.6 \text{ cm} \)
(4) Perimeter of a rectangle STUV
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 3 + 2 \times 2 \)
= \( 6 + 4 \)
= \( 10 \text{ cm} \)
(5) Perimeter of a triangle LMN
= \( 1.5 + 2.5 + 2 \)
= \( 6 \text{ cm} \)
In simple words: For each shape on the graph paper, measure its sides by counting the grid lines. Then, use the appropriate perimeter formula (2x(length+breadth) for rectangles, sum of sides for triangles) to calculate and write down its perimeter.

🎯 Exam Tip: When using graph paper, count the units carefully for each side length. Accuracy in measurement and applying the correct perimeter formula for each shape are key to solving such problems.

Area: Revision

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र ग्राफ पेपर पर विभिन्न आकृतियों जैसे ABCD, MNRS, EFGH, PQRS और IJKL को दर्शाता है। प्रत्येक आकृति में 1 सेमी के कितने वर्ग हैं, यह गिनकर उनका क्षेत्रफल ज्ञात करना है।

Of the figures given above, figure ABCD has six squares of 1 cm each inside it. It means that its area is 6 sq cm.

In the same way, count the squares in each figure and write its area.
(1) Area of MNRS = [ ] sq cm
(2) Area of EFGH = [ ] sq cm
(3) Area of PQRS = [ ] sq cm
(4) Area of IJKL = [ ] sq cm

Atul: Sir, why is the unit for area written as sq cm? We measure the sides in centimetres.

Teacher : Centimetre is a standard unit of length. In order to measure area, we need a standard unit of area. For this, a square with a side 1 cm is taken as the standard unit. The area of this square is 1 square centimetre. That is why this unit is written as sq cm, in short.

To measure large areas like fields, parks and playgrounds, a square with side 1 m, that is, an area of 1 sq m, is taken as the standard unit.

To measure the areas of talukas or districts, a square with side 1km, or 1sq km is the standard unit used.

Formula For The Area Of A Rectangle

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र ग्राफ पेपर पर एक आयत ABCD दिखाता है, जिसकी लंबाई 5 सेमी और चौड़ाई 3 सेमी है। आयत के अंदर 1 सेमी भुजा वाले वर्गों को दर्शाया गया है, जिससे छात्रों को आयत का क्षेत्रफल समझने में मदद मिलेगी।

(1) In the rectangle ABCD given alongside, 1 cm divisions were marked off on each side. The points on opposite sides were joined as shown in the figure. The length of the sides of each square thus created is 1cm. Therefore, the area of each square is 1 sq cm.

In ABCD, 3 rows with 5 squares each have been created.
The number of squares in rectangle ABCD is \( 3 \times 5 = 15 \).
Therefore, the area of rectangle ABCD is 15 sq cm.
Here, the length of the figure is 5 cm and its breadth is 3 cm.
Note that the product of 3 and 5 is 15.

(2) In the rectangle with sides 4 cm and 2 cm, make squares of 1 sq cm each as shown above. Count the number of squares.

Note that here too, the number of squares formed are the same as the product of the length and width of the rectangle.

Therefore, The area of a rectangle = \( \text{length} \times \text{breadth} \)

Formula For The Area Of A Square

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र ग्राफ पेपर पर एक वर्ग MNRS दिखाता है, जिसकी प्रत्येक भुजा 3 सेमी लंबी है। वर्ग के अंदर 1 सेमी भुजा वाले वर्गों को दर्शाया गया है, जिससे छात्रों को वर्ग का क्षेत्रफल समझने में मदद मिलेगी।

(1) Look at the square given alongside. The side of the square is 3 cm long. 9 squares of 1 cm each are formed within this square.

Therefore, the area of this square is 9 sq cm.

Here, there are 3 rows with 3 squares each, i.e., there are \( 3 \times 3 = 9 \) squares.
The length of each side of the square is 3 cm.
The product of two sides of the square is \( 3 \times 3 = 9 \).

(2) Measure the area of a square with side 5 cm, in the same way.
The answer will be 25 sq cm.
Note that \( 5 \times 5 = 25 \)

Therefore, The area of a square = \( \text{length of a side} \times \text{length of a side} \)

It is not necessary to divide a square or rectangle into small squares every time you calculate their area. The advantage of a formula is that you can calculate the area simply by substituting the appropriate values.

Word Problems

Example (1) What is the area of a rectangle of length 20 cm and width 15 cm?
Answer: Area of a rectangle = \( \text{length} \times \text{breadth} \)
= \( 20 \times 15 \)
= \( 300 \)
Therefore, the area of the rectangle is 300 sq cm.
In simple words: The area of a rectangle is found by multiplying its length by its breadth. For a rectangle with a length of 20 cm and a width of 15 cm, the area is 300 sq cm.

🎯 Exam Tip: Always use square units (e.g., sq cm, sq m) when stating an area. Remember to multiply length and breadth directly.

Example (2) A wall that is 4 m long and 3 m wide has to be painted. If the labour charges are Rs. 25 per sq m, what is the cost of labour for painting this wall?
Answer: First let us calculate the area of the wall to be painted.
Area of the wall = \( \text{length of the wall} \times \text{breadth of the wall} \)
= \( 4 \times 3 \)
= \( 12 \)
Thus, the area of the wall is 12 sq m.
Labour cost of 1 sq m is Rs. 25.
So the labour cost for 12 sq m will be
= \( 12 \times 25 \)
= \( 300 \)
The cost of labour for painting the wall will be 300 Rs..
In simple words: Calculate the area of the wall by multiplying its length and width. Then, multiply this area by the labor cost per square meter to find the total labor cost.

🎯 Exam Tip: Clearly identify the two main steps: calculating the area, and then calculating the total cost using the given rate. Ensure the units for area and rate match.

Example (3) What will be the area of a square with sides 15 cm?
Answer: Area of a square = \( \text{length of side} \times \text{length of side} \)
= \( 15 \times 15 \)
= \( 225 \)
The area of the square is 225 sq cm.
In simple words: To find the area of a square, multiply the length of one side by itself. For a side length of 15 cm, the area is 225 sq cm.

🎯 Exam Tip: The area of a square is simply the square of its side length. Do not confuse it with the perimeter. Always use square units for area.

Example (4) One side of a square room is 4 m. If the cost of labour for laying 1 sq m of the floor is 35 Rs., what will be the total cost of labour?
Answer: First we must find the area of the square room.
Area of the square room = \( \text{length of side} \times \text{length of side} \)
= \( 4 \times 4 \)
= \( 16 \)
Therefore, the area of the square room is 16 sq m.
The labour cost of laying 1 sq m of flooring is 35 Rs..
Therefore, the cost of laying 16 sq m of flooring is
= \( 16 \times 35 \)
= \( 560 \text{ Rs.} \).
In simple words: First, calculate the area of the square room. Then, multiply this area by the labor cost per square meter to find the total labor cost for laying the floor.

🎯 Exam Tip: This problem combines area calculation with cost calculation. Ensure the area unit (sq m) matches the cost rate unit (Rs. per sq m) for direct multiplication.

Perimeter And Area Problem Set 49 Additional Important Questions And Answers

Question 1. Devendra walks five rounds of a square garden everyday. If the side of the garden is 150 m, how many kilometres does Devendra walk every morning?
Answer: Perimeter of a square garden
= \( 4 \times \text{one side of the garden} \)
= \( 4 \times 150 \)
= \( 600 \text{ m} \)
In 5 rounds walking
= \( 5 \times 600 \)
= \( 3000 \text{ m} \)
= \( 3 \text{ km} \)
Therefore, Devendra walks 3 km every morning.
In simple words: First, calculate the perimeter of the square garden (one round). Then, multiply that distance by the number of rounds (5) and convert the total meters to kilometers.

🎯 Exam Tip: Remember to convert the final answer to the requested unit (kilometers in this case). Carefully perform the multiplication for multiple rounds and the unit conversion.

Question 2. The length of a rectangular play ground is 75 m and its breadth is 50 m. Rupali walks four rounds. How many kilometres did she walk?
Answer: Perimeter of rectangle
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 75 + 2 \times 50 \)
= \( 150 + 100 \)
= \( 250 \text{ m} \)
In 4 rounds walking
= \( 4 \times 250 \)
= \( 1000 \text{ m} \)
= \( 1 \text{ km} \)
Therefore, Rupali walked 1 km.
In simple words: First, find the perimeter of the rectangular playground for one round. Then, multiply this perimeter by the number of rounds (4) to get the total distance in meters, and finally convert it to kilometers.

🎯 Exam Tip: This question tests both perimeter calculation and unit conversion. Ensure both steps are done accurately and the final answer is in kilometers as requested.

Question 3. Length of the rectangle is 10 cm and its breadth is 8 cm and one square is side 9 cm. Whose perimetre is more? By how much?
Answer: Perimeter of a rectangle
= \( 2 \times \text{length} + 2 \times \text{breadth} \)
= \( 2 \times 10 + 2 \times 8 \)
= \( 20 + 16 \)
= \( 36 \text{ cm} \) (i)
Perimeter of a square
= \( 4 \times \text{length of side} \)
= \( 4 \times 9 \)
= \( 36 \text{ cm} \) (ii)
From (i) and (ii) perimeter of both is equal.
In simple words: Calculate the perimeter of the rectangle (36 cm) and the square (36 cm) separately. By comparing the two perimeters, we find that they are both equal.

🎯 Exam Tip: When comparing perimeters of different shapes, calculate each perimeter accurately using its specific formula. Clearly state the calculated values and your comparison conclusion.