Perimeter and Area
Overview
Perimeter is the total length of the boundary of a closed figure, while area is the measure of the region enclosed by it. This chapter covers perimeter and area of squares, rectangles, triangles, parallelograms, and circles. Students learn to apply these concepts to solve real-life problems such as fencing a field, tiling a floor, or finding the cost of painting a wall. Understanding the difference between perimeter and area is the foundation of this chapter.
Typed Notes
Perimeter of Rectangles and Squares
Perimeter is the total distance around a shape. For a rectangle with length l and breadth b, Perimeter = 2(l + b). For a square with side s, Perimeter = 4s. These formulas are used in everyday situations like finding the length of wire needed to fence a rectangular garden or the amount of ribbon needed to border a square photo frame. Always use the same unit for all measurements before calculating perimeter.
Area of Rectangles, Squares, Parallelograms and Triangles
Area of a rectangle = l × b, and area of a square = s × s = s². A parallelogram has the same area formula as a rectangle when we use its perpendicular height: Area = base × height. A diagonal of a parallelogram divides it into two equal triangles, so Area of triangle = ½ × base × height. These formulas help solve problems like finding the area of a field, the amount of paint needed for a wall, or the number of tiles required to cover a floor.
Circles — Circumference and Area
A circle's boundary length is called its circumference. Circumference = 2πr, where r is the radius and π = 22/7 (approximately). The diameter d = 2r, so Circumference = πd. Area of a circle = πr². For example, a circular park of radius 7 m has circumference = 2 × 22/7 × 7 = 44 m and area = 22/7 × 7 × 7 = 154 m². Circles appear in wheels, coins, clocks, and many real-life objects, making these formulas very practical.
Conversion of Units and Mixed Problems
When solving area and perimeter problems, units must be consistent. Common conversions: 1 m = 100 cm, 1 km = 1000 m, 1 m² = 10,000 cm², 1 hectare = 10,000 m². Mixed problems may involve finding the cost of fencing (using perimeter) or the cost of flooring (using area). Always identify whether the problem asks for boundary length (perimeter) or surface covered (area) before applying the formula. Reading the problem carefully avoids the common mistake of mixing up the two concepts.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Perimeter of a rectangle = 2 × (length + breadth); Area = length × breadth.
- 02Perimeter of a square = 4 × side; Area = side × side.
- 03Area of a parallelogram = base × height; the height is always perpendicular to the base.
- 04Area of a triangle = ½ × base × height; a triangle is half of a parallelogram with the same base and height.
- 05Circumference of a circle = 2πr; Area of a circle = πr², where π ≈ 22/7 or 3.14.
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
A rectangular park is 45 m long and 30 m wide. Find its perimeter and the cost of fencing it at ₹20 per metre.
Find the area of a triangle whose base is 14 cm and height is 9 cm.
A parallelogram has a base of 12 cm and a perpendicular height of 7 cm. Find its area.
Find the circumference and area of a circle with radius 14 cm. (Use π = 22/7)
A square floor of side 8 m is to be tiled with square tiles of side 50 cm. How many tiles are needed?
Perimeter measures the boundary of a figure while area measures the surface it covers. Key formulas include: Rectangle — 2(l+b) and l×b; Square — 4s and s²; Parallelogram — base×height; Triangle — ½×base×height; Circle — 2πr and πr². Unit conversions are essential for accuracy. These concepts are widely used in real-life situations like construction, gardening, and design.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is the area of a rectangle with length 9 cm and breadth 5 cm?
Q2.The circumference of a circle is 44 cm. What is its radius? (π = 22/7)
Q3.Which formula gives the area of a triangle?
Q4.A square has a perimeter of 36 cm. What is its area?
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