NCERT Solutions & Concepts for Class 7 Maths Exercise 11.1: Perimeter and Area

Welcome, future mathematicians, to YoLearn AI Tutor! In this chapter of CBSE Class 7 Maths, we dive into the foundational principles of geometry with perimeter and area ex 11 1 class 7 ncert. Have you ever wondered how much fencing is needed to surround a beautiful park, or how much grass seed is required to cover its entire surface? That is exactly what we are going to learn! Perimeter is the boundary, while area is the region enclosed within. In Exercise 11.1, you will master calculating the perimeter and area of squares and rectangles, finding missing dimensions when area is given, and solving real-world cost-estimation problems. By learning with YoLearn, you will gain the visual intuition to break down complex word problems step-by-step. Let's make these calculations effortless and intuitive!

Understanding Perimeter vs. Area of Squares and Rectangles

To master perimeter and area ex 11 1 class 7 ncert, we must first build a solid visual understanding of what these terms represent. Let's use a simple analogy: imagine a rectangular garden. The boundary fence you build around this garden represents its Perimeter. It is a one-dimensional measure of length, calculated by adding the lengths of all outer sides. For a rectangle with length ($l$) and breadth ($b$), the perimeter formula is $2 \times (l + b)$. For a square with side length ($s$), the perimeter is simply $4 \times s$.

On the other hand, the green grass carpet that covers the entire ground inside that fence represents the Area. It is a two-dimensional measure of surface, expressed in square units (like $cm^2$ or $m^2$). The area of a rectangle is found by multiplying its length and breadth ($l \times b$). For a square, since all sides are equal, the area is side times side ($s \times s$ or $s^2$). Always check that both dimensions are in the same unit before doing any multiplication!

How to Find a Missing Dimension (Step-by-Step)

  1. Identify the Given Values — Read the problem carefully to find the values already provided, such as Area, Perimeter, Length, or Breadth. Note them down clearly with their respective units.
  2. Check and Convert Units — Ensure all given values are in the same units (e.g., both in cm or both in meters). If one is in cm and another is in meters, convert using 1 m = 100 cm before proceeding.
  3. Select the Correct Formula — If Area and Length are given and you need to find the Breadth of a rectangle, write down the formula: Area = Length × Breadth.
  4. Rearrange and Calculate — Rearrange the formula to isolate the missing variable: Breadth = Area ÷ Length. Substitute the values and calculate the final numerical answer.

Avoid the Unit Trap in Your Board Exams!

A very common mistake students make in class 7 maths perimeter and area ex 11 1 is mixing up units of length and units of area, or performing calculations with different units.

  • Perimeter is a measure of length, so its unit is always linear (e.g., $cm, m, km$).
  • Area is a measure of surface, so its unit is always squared (e.g., $cm^2, m^2, km^2$).
  • If a question asks you to find the cost of tiling a floor at ₹20 per $m^2$, but your dimensions are given in $cm$, convert the dimensions to meters first before calculating the area! This prevents massive calculation errors.

Practice Questions with Solutions

  • Q: A rectangular plot of land is 500 m long and 300 m wide. Find (i) its area, and (ii) the cost of the land if 1 m² of the land costs ₹10,000. A: Step 1: Write down the given values. Length ($l$) = 500 m, Breadth ($b$) = 300 m. Step 2: Calculate the Area. Area of rectangle = $l \times b$ Area = $500 \times 300 = 1,50,000\text{ m}^2$. Step 3: Calculate the cost. Cost of 1 m² of land = ₹10,000. Total cost = Area $\times$ Cost per m² Total cost = $1,50,00,00 = 1,50,000 \times 10,000 = ₹1,50,00,00,000$. Final answer: Area is $1,50,000\text{ m}^2$ and the total cost is ₹1,50,00,00,000.
  • Q: Find the area of a square park whose perimeter is 320 m. A: Step 1: Write down the given value. Perimeter of square = 320 m. Step 2: Find the side of the square. Perimeter of square = $4 \times \text{side}$ $320 = 4 \times \text{side}$ $\text{side} = 320 / 4 = 80\text{ m}$. Step 3: Calculate the Area. Area of square = $\text{side} \times \text{side}$ Area = $80 \times 80 = 6,400\text{ m}^2$. Final answer: The area of the square park is $6,400\text{ m}^2$.
  • Q: Find the breadth of a rectangular plot of land, if its area is 440 m² and the length is 22 m. Also find its perimeter. A: Step 1: Identify given values. Area = 440 m², Length ($l$) = 22 m. Step 2: Find the breadth ($b$). Area = $l \times b$ $440 = 22 \times b$ $b = 440 / 22 = 20\text{ m}$. Step 3: Calculate the Perimeter. Perimeter = $2(l + b)$ Perimeter = $2(22 + 20) = 2(42) = 84\text{ m}$. Final answer: Breadth is 20 m and Perimeter is 84 m.
  • Q: The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area. A: Step 1: Identify given values. Perimeter = 100 cm, Length ($l$) = 35 cm. Step 2: Find the breadth ($b$) using the perimeter formula. Perimeter = $2(l + b)$ $100 = 2(35 + b)$ Divide both sides by 2: $50 = 35 + b$ $b = 50 - 35 = 15\text{ cm}$. Step 3: Calculate the Area. Area = $l \times b$ Area = $35 \times 15 = 525\text{ cm}^2$. Final answer: Breadth is 15 cm and Area is $525\text{ cm}^2$.

Frequently Asked Questions

What is the primary difference between perimeter and area?

Perimeter is the length of the boundary line enclosing a closed figure, measured in linear units like meters. Area is the total space enclosed within that boundary, measured in square units like square meters.

How do we convert square meters (m²) to square centimeters (cm²)?

Since 1 m = 100 cm, a square meter is calculated as 100 cm multiplied by 100 cm, which equals 10,000 cm². Therefore, to convert m² to cm², you must multiply the value by 10,000.

What should I do if the length is in meters and breadth is in centimeters?

You must convert both measurements to the same unit before calculating. It is usually easiest to convert the meter value to centimeters by multiplying by 100, or convert centimeters to meters by dividing by 100.