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Encapsulate
math
PERIMETER ANd AREA

Perimeter Area

The total length of the boundary of a simple The measurement of surface enclosed by a
closed figure is called its perimeter. closed figure is called its area.

1. Perimeter of a rectangle = 2 (length + breadth) 1. Area of a rectangle = length × breadth
Length Length
Breadth Breadth

2. Perimeter of regular polygons:
 Perimeter of a square = 4 × length of a side 2. Area of a square = Side × side
Side
Side

 Perimeter of an equilateral triangle
= 3 × length of a side 3. Area of a triangle = 1 of area of rectangle made
2
on the same base and having the same height that
of the rectangle.
 Perimeter of other regular polygons
4. Area of Irregular shapes
Polygon Sides Perimeter Count the total number of fully, half and more than
Pentagon 5 5 × length of side half-filled squares.
Hexagon 6 6 × length of side 1 1
 Exact half-filled squares has area = sq. unit.
Heptagon 7 7 × length of side 2 2
Octagon 8 8 × length of side  Ignore less than half-filled squares (or 0 sq. unit).
Nonagon 9 9 × length of side  More than half-filled square has area = 1 sq. unit.
Decagon 10 10 × length of side  Area of 1 completely-filled square = 1 sq. unit.

Brain Sizzlers

1. Aman’s father had a rectangular land with a perimeter of 40 m. He divided this land into six identical
squares by drawing three lines to start organic farming. If he grew vegetables in the shaded area, find the area
of the land used to grow vegetables.
A B

D C
2. On an A4 sheet of paper, draw a rectangular border that is 2 cm from the top and bottom and 1 cm from the
left and right sides. What is the perimeter of the border? What will be the marginal area of the sheet?

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