Maharashtra Board Class 5 Maths Chapter 12 Perimeter and Area Set 48 Solutions

Problem Set 48 Class 5 Maths Chapter 12 Perimeter and Area Question Answer Maharashtra Board

Perimeter And Area Class 5 Problem Set 48 Question Answer Maharashtra Board

Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 12 Perimeter And Area Problem Set 48 Textbook Exercise Important Questions And Answers.

Std 5 Maths Chapter 12 Perimeter And Area

Question 1. Write the perimeter of each figure in the box given below it.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक चतुर्भुज आकृति है जिसके चार भुजाएँ हैं। शीर्ष भुजा 7 सेमी, निचली भुजा 20 सेमी, बाईं भुजा 14 सेमी और दाईं भुजा 16 सेमी है। यह एक समलंब चतुर्भुज की तरह दिखता है।
Answer:Perimeter of the figure = 20 + 16 + 7 + 14 = 57 cm Therefore, 57 cm
In simple words: The perimeter of the given four-sided figure is found by adding the lengths of all its four sides: 20 cm, 16 cm, 7 cm, and 14 cm, which totals 57 cm.

🎯 Exam Tip: Remember that perimeter is the total length of the boundary of a closed figure. Ensure all side lengths are added correctly for irregular shapes.

 

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक पंचभुज आकृति है जो एक घर के आकार की है। इसका आधार 12 मीटर है, दो सीधी खड़ी भुजाएँ प्रत्येक 18 मीटर हैं, और ऊपर की दो तिरछी भुजाएँ प्रत्येक 8 मीटर हैं।
Answer:Perimeter of the figure = 12 + 18 + 8 + 8 + 18 = 64m Therefore, 64m
In simple words: The perimeter of this house-shaped pentagon is calculated by summing its five side lengths: 12m, 18m, 8m, 8m, and 18m, resulting in 64 meters.

🎯 Exam Tip: For complex polygons, always trace each side once to ensure no side is missed or counted twice when calculating the perimeter.

 

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक षट्भुज आकृति है जिसकी भुजाएँ असमान हैं। इसमें दो भुजाएँ 10 सेमी की, दो भुजाएँ 8 सेमी की और दो भुजाएँ 6 सेमी की हैं।
Answer:Perimeter of the figure = 10 + 6 + 6 + 10 + 8 + 8 = 48 cm Therefore, 48 cm
In simple words: The perimeter of this hexagon is found by adding all its six side lengths: 10 cm, 6 cm, 6 cm, 10 cm, 8 cm, and 8 cm, which sums up to 48 cm.

🎯 Exam Tip: Pay close attention to each side's measurement when calculating the perimeter of irregular polygons to avoid errors.

 

Question 2. If a square of side 1 cm is cut out of the corner of a larger square with side 3 cm (see the figure), what will be the perimeter of the remaining shape?

ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में एक 3 सेमी x 3 सेमी का वर्ग दिखाया गया है। दूसरे चित्र में, इस बड़े वर्ग के एक कोने से 1 सेमी x 1 सेमी का एक छोटा वर्ग काट दिया गया है, जिसके परिणामस्वरूप एक L-आकार की आकृति बनी है।
Answer:Perimeter = 2 + 3 + 3 + 2 + 1 + 1 = 12 cm Therefore, 12 cm
In simple words: When a 1 cm corner square is cut from a 3 cm square, the original perimeter changes. The new perimeter is calculated by adding the lengths of all the exposed sides of the L-shaped figure, which comes out to be 12 cm.

🎯 Exam Tip: For shapes with cut-outs, carefully identify all the new boundary segments that contribute to the perimeter. Sometimes, cutting a corner can maintain or even increase the perimeter, depending on the cut.

 

Formula For The Perimeter Of A Rectangle

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक सामान्य आयत को दर्शाता है। इसकी ऊपरी और निचली भुजाएँ 'लंबाई' (length) के रूप में चिह्नित हैं, और बाईं व दाईं भुजाएँ 'चौड़ाई' (breadth) के रूप में चिह्नित हैं। Perimeter = length + breadth + length + breadth Opposite sides of a rectangle are of the same length. So, the perimeter of a rectangle = twice the length + twice the breadth = 2 × length + 2 × breadth

Perimeter of a rectangle = 2 × length + 2 × breadth

Example : The length of the rectangle below is 7 cm and its breadth, 3 cm. Let us find its perimeter.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक आयत PQRS को दर्शाता है। भुजा PQ (निचली) और SR (ऊपरी) को 7 सेमी लेबल किया गया है, जबकि भुजा PS (बाईं) और QR (दाईं) को 3 सेमी लेबल किया गया है। Perimeter of rectangle PQRS = 2 × length + 2 × breadth = 2 × 7 + 2 × 3 = 14 + 6 = 20 Therefore, the perimeter of the rectangle is 20 cm.

Formula For The Perimeter Of A Square

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक साधारण वर्ग को दर्शाता है, जिसमें कोई विशिष्ट आयाम नहीं दिए गए हैं, बस वर्ग की मूलभूत आकृति। The lengths of all the sides of a square are equal. Therefore, the perimeter of a square = four times the length of one of its sides.

Perimeter of a square = 4 × the length of one side

Example : The length of one side of a square is 6 cm. Find its perimeter. The perimeter of a square is four times the length of one side.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक वर्ग को दर्शाता है जिसकी एक भुजा को 6 सेमी के रूप में चिह्नित किया गया है, यह दर्शाता है कि वर्ग की सभी भुजाएँ 6 सेमी लंबी हैं। Perimeter of a square = 4 × length of one side = 4 × 6 = 24 Therefore, the perimeter of the square is 24 cm.

Word Problems

Example (1) The length of a rectangular park is 100 m, while its width is 80 m. What is its perimeter?

Answer:Perimeter of the rectangle = 2 × length + 2 × breadth = 2 × 100 + 2 × 80 = 200 + 160 = 360 The perimeter of the rectangular park is 360 m.
In simple words: To find the perimeter of the rectangular park, we use the formula 2(length + breadth). With a length of 100 m and width of 80 m, the perimeter is 2(100 + 80) = 2(180) = 360 m.

🎯 Exam Tip: Always state the formula before substituting values and show each step of the calculation clearly.

 

Example (2) How much wire will be needed to put a triple fence around a square plot with side 30 m? What will be the total cost of the wire at Rs. 70 per metre ?

Answer:To put a single fence around the square plot, we need to find its perimeter. Perimeter of a square = 4 × length of one side = 4 × 30 = 120 The perimeter of the square plot is 120 metres. Since the fence is to be a triple fence, we must triple the perimeter. 120 x 3 = 360 m of wire will be needed. Now let us find out how much the wire will cost. One metre of wire costs Rs. 70. Therefore, the cost of 360 m of wire will be 360 × 70 = 25, 200. The total cost of wire for putting a triple fence around the plot will be Rs. 25,200.
In simple words: First, calculate the perimeter of the square plot (4 x 30m = 120m). For a triple fence, multiply this perimeter by 3 (120m x 3 = 360m). Finally, calculate the total cost by multiplying the total wire length by the cost per meter (360m x Rs. 70 = Rs. 25,200).

🎯 Exam Tip: Break down multi-step problems into smaller, manageable parts. Clearly show each calculation step, especially for perimeter and cost, to earn full marks.

 

Perimeter And Area Problem Set 48 Additional Important Questions And Answers

Question 1.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक आयताकार आकृति है जिसकी ऊपरी और निचली भुजाएँ 6 सेमी लंबी हैं, और बाईं और दाईं भुजाएँ 2 सेमी लंबी हैं।
Answer:Perimeter of the figure = 2 + 6 + 2 + 6 = 16 cm Therefore, 16 cm
In simple words: The perimeter of this rectangular figure is found by adding all its four sides: 2 cm, 6 cm, 2 cm, and 6 cm, which totals 16 cm.

🎯 Exam Tip: Always double-check that all sides are included in the sum when calculating the perimeter of any polygon.

 

Question 2.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक वर्ग को दर्शाता है जहाँ इसकी चारों भुजाएँ, शीर्ष, बाईं, दाईं और निचली, प्रत्येक 3 सेमी लंबी चिह्नित हैं।
Answer:Perimeter of the figure = 3 + 3 + 3 + 3 = 12 cm Therefore, 12 cm
In simple words: The perimeter of this square is calculated by adding the lengths of its four equal sides, each being 3 cm, resulting in a total of 12 cm.

🎯 Exam Tip: For a square, remember the shortcut formula: Perimeter = 4 × side. This can save time in calculations.

 

Question 3.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक समकोण त्रिभुज को दर्शाता है। इसकी लंबवत भुजा 5 सेमी, क्षैतिज भुजा 12 सेमी, और कर्ण (सबसे लंबी भुजा) 13 सेमी लंबी है।
Answer:Perimeter of the figure = 12 + 13 + 5 = 30 cm Therefore, 30 cm
In simple words: The perimeter of this triangle is calculated by adding the lengths of its three sides: 12 cm, 13 cm, and 5 cm, which sum up to 30 cm.

🎯 Exam Tip: The perimeter of a triangle is simply the sum of its three side lengths. Ensure all three lengths are correctly identified and added.

 

Question 4. If four squares of side 1 cm is cut out of all the corners of a larger square with side 4 cm (see the figure), what will be the perimeter of the remaining shape?

ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में एक 4 सेमी x 4 सेमी का वर्ग दिखाया गया है। दूसरे चित्र में, इस बड़े वर्ग के चारों कोनों से 1 सेमी x 1 सेमी के चार छोटे वर्ग काट दिए गए हैं, जिसके परिणामस्वरूप एक क्रॉस-जैसी आकृति बनी है जिसमें कई 1 सेमी और 2 सेमी के छोटे खंड हैं।
Answer:Perimeter = 2 + 1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 = 16 cm Therefore, 16 cm
In simple words: When four 1 cm corner squares are cut from a 4 cm square, the original perimeter of the 4 cm square (16 cm) remains the same. Each corner cut replaces two 1 cm outer edges with two 1 cm inner edges, effectively not changing the total boundary length.

🎯 Exam Tip: When parts are cut from a shape, analyze how the cuts affect the boundary. Often, if a square corner is cut, the perimeter remains unchanged if the cut-out forms new edges of equal total length to the removed edges.

Class 5 Maths Solution Maharashtra Board