# FIND AREA AND PERIMETER BY COUNTING SQUARES

Example 1 :

Find the area of the figure given below. Solution :

By observing the figure, it is a triangle.

Then, AC  =  base and BD  =  height

There are 4 units for the base and 3 units for height.

Finding the area :

Area of a triangle  =  1/2 × base × height

=  1/2 × 4 × 3

Area  =  6 sq.units

Example 2  :

Find the area and perimeter of the figure given below. Solution :

By observing the figure, it is a square.

Then, HG  =  GF  =  EF  =  EH  =  side

There are 5 units for the side.

Finding the area :

Area of a square  =  side2

=  52

Area  =  25 sq.units

Finding the Perimeter :

Perimeter of a square  =  4a

=  4(5)

Perimeter  =  20 units

Example 3  : Solution :

By observing the figure, it is a circle.

Then, OA  =  radius

There are 2 units for radius.

Finding the area :

Area of a circle  =  πr2

=  π(22)

=  4π

Area  =  4π sq.units

Draw the figure in a coordinate plane and find its area and perimeter.

Example 4  :

Triangle defined by A(3, 4), B(7, 4), and C(5, 7)

Solution :

By plotting the given points on the graph, we get Now, there is a triangle.

Then, AB  =  base and CD  =  height

There are 4 units for the base and 3 units for height.

Finding the area :

Area of a triangle  =  1/2 × base × height

=  1/2 × 4 × 3

Area  =  6 sq.units

Example 5  :

Triangle defined by R(-2, -3), S(6, -3), and T(5, 4)

Solution :

By plotting the given points on the graph, we get Now, there is a triangle.

Then, RS  =  base and TQ  =  height

There are 8 units for the base and 7 units for height.

Finding the area :

Area of a triangle  =  1/2 × base × height

=  1/2 × 8 × 7

Area  =  28 sq.units

Example 6  :

Rectangle defined by L(-2, -4), M(-2, 1), N(7, 1) and P(7, -4)

Solution :

By plotting the given points on the graph, we get Now, there is a rectangle.

Then, LP  =  length and NP  =  width

There are 9 units for the length and 5 units for width.

Finding the area :

Area of a rectangle  =  length × width

=  9 × 5

Area  =  45 sq.units

Finding the perimeter :

Perimeter of a rectangle  =  2(length + width)

=  2(9 + 5)

=  2(14)

Perimeter  =  28 units

Example 7  :

Square defined by W(5, 0), X(0, 5), Y(-5, 0) and Z(0, -5)

Solution :

By plotting the given points on the graph, we get Now, there is a square.

But, we couldn’t calculate XY  =  YZ (side)

So, we are using the diagonals.

Here, d  =  10 units

Finding the area :

Area of square using diagonals  =  1/2 × d2

=  1/2 × 102

=  1/2 × 100

Area  =  50 sq.units

Finding the perimeter :

Perimeter of a square using diagonals  =  4 × √(d2/2)

=  4 × √(102/2)

=  4 × √100/2

=  4 × √50

=  4 × 5√2

=  20√2

Perimeter  =  20√2 units

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