### Mathematics Class VII

Integers
Fractions and Decimals
Exponents and Powers
Algebraic Equations
Simple Linear Equations
Lines and Angles
Comparing Quantities
Congruence of Triangles
Rational Numbers
Perimeter and Area
Data Handling
Practical Geometry
Symmetry
Visualising Solid Shapes

# Squares And Rectangles

##### Area and Perimeter of Square

Square is a quadrilateral, with four equal sides.

Area = Side × Side

Perimeter = 4 × Side

Example

Find the area and perimeter of a square-shaped cardboard whose length is 5 cm.

Solution

Area of square = (side)2

= (5)2

= 25 cm2

Perimeter of square = 4 × side

= 4 × 5

= 20 cm

##### Area and Perimeter of Rectangle

The rectangle is a quadrilateral, with equal opposite sides.

Example

What is the length of a rectangular field if its width is 20 ft and Area is 500 ft2?

Solution

Area of rectangular field = length × width

500 = l × 20

l = 500/20

l = 25 ft

Example

What will be the area of each triangle if we draw two diagonals of a square with side 7 cm?

Solution

Area of square = 7 × 7

= 49 cm2

The area of each triangle = 1/4 (Area of the square)

= 1/4 × 49

= 12.25 cm2

##### Congruent Parts of Rectangles

Two parts of a rectangle are congruent to each other if the area of the first part is equal to the area of the second part.

Example

The area of each congruent part = 1/2 (Area of the rectangle)

= 1/2 (l × b) cm2

=1/2 (4 × 3) cm2

= 1/2 (12) cm2

= 6 cm2

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