Class 7 Maths Chapter 16 Perimeter and Area PDF
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Summary
This document is a chapter from a class 7 math textbook about perimeter and area, covering topics such as calculating the costs of fencing and ploughing fields, finding areas of parallelograms and triangles, and understanding circumference and area of circles.
Full Transcript
# Chapter 16: Perimeter and Area ## 16.1 Neelam and Rakesh's Fields Neelam and Rakesh made fencing of barbed wires around their field. * Neelam's field is rectangular, with a length of 180 meters and a width of 60 meters * Rakesh's field is square, with sides of 120 meters. The cost of fencing i...
# Chapter 16: Perimeter and Area ## 16.1 Neelam and Rakesh's Fields Neelam and Rakesh made fencing of barbed wires around their field. * Neelam's field is rectangular, with a length of 180 meters and a width of 60 meters * Rakesh's field is square, with sides of 120 meters. The cost of fencing is Rs. 12 per meter. **Question:** On whose field would the cost of fencing be maximum? **Answer:** The cost of fencing would be maximum on Neelam's field, as it has a larger perimeter. **Calculation:** * **Neelam's Field perimeter:** 2 * (length + width) = 2 * (180 + 60) = 480 meters * **Rakesh's Field perimeter:** 4 * side = 4 * 120 = 480 meters The cost of ploughing is Rs. 100 per square meter. **Question:** Which field would cost the most to plough? **Answer:** Rakesh's field would cost the most to plough, as it has a larger area. **Calculation:** * **Neelam's Field area:** length * width = 180 * 60 = 10800 square meters * **Rakesh's Field area:** side² = 120² = 14400 square meters ## 16.2 Area of a Parallelogram * Opposite sides of a parallelogram are equal and parallel. * The area of a parallelogram is calculated by multiplying the base by the height. **Activity:** 1. Draw three parallelograms of different measures. 2. Draw a perpendicular from one vertex to the opposite side of the parallelogram. 3. Cut out the triangle formed by the vertex and the perpendicular and move it to the opposite side to form a rectangle. 4. Calculate the area of the rectangle and compare it to the area of the parallelogram. **Conclusion:** The area of the rectangle and the parallelogram are equal. **Formula:** Area of Parallelogram = Base * Height (square units) ## 16.2.1 Path Ways **How to calculate the area of a path around a figure:** * Area of Path = Area of Figure including Path - Area of Figure without Path. * Area of Path parallel to length/breadth: Length/breadth of Path * Breadth/length * Area of Paths intersecting: Total Area of Path - Area of Intersection ## 16.3 Area of Triangle * The area of a triangle is half the area of the parallelogram generated from it. * **Formula:** Area of Triangle = 1/2 * Base * Height ## 16.4 Circumference of a Circle * The circumference of a circle is the distance around it. * **Formula:** Circumference = πd = 2πr, where d is the diameter and r is the radius. ## 16.4.2 Area of Circle * The area of a circle is the space it occupies. * **Formula:** Area = πr², where r is the radius.
