## About "Area of a parallelogram"

Area of a parallelogram :

A parallelogram is a quadrilateral in which opposite sides are parallel and equal in length. In other words opposite sides of a quadrilateral are equal in length,then the quadrilateral is called a parallelogram.

Area of parallelogram = base x height

## Relationship between a rectangle and parallelogram

Draw a large parallelogram on grid paper. Cut out the parallelogram.

Cut the parallelogram along the dashed segment as shown. Then move the triangular piece to the other side of the parallelogram.

From here we can observer that

base of parallelogram = length of the rectangle

height of parallelogram = width of the rectangle

area of parallelogram = area of the rectangle

Example 1 :

A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 ⅓ square yards. The height of each parallelogram is 1 ⅓ yards.

a. How long is the base of each parallelogram?

Solution :

(a) Since the given parallelograms are congruent area of two parallelogram will be equal.

Combined area of parallelogram =  9 ⅓ square yards

Area of one parallelogram = (28/3) / 2

=  14/3

Area of parallelogram = base x height

base x   1 ⅓  =  14/3

base x 4/3  =  14/3

base  =  (14/3) / (4/3) ==> 7/2 ==> 3½ yards

Example 2 :

A watercolor painting is 20 inches long by 9 inches wide. Ramon makes a border around the watercolor painting by making a mat that adds 1 inch to each side of the length and the width.What is the area of the mat?

Solution :

Length of the mat = 20 + 1 + 1 = 22 inches

breadth of the mat = 9 + 1 + 1 = 11 inches

The area of the mat

= total area added - the original area of the water color

=  (22 x 11) - (20 x 9)

=  242 - 180

=  62 square inches

Example 3 :

Find the base of a parallelogram if its area is 40 cm² and its altitude is 15 cm.

Solution :

Area of a parallelogram  = 40 cm²

b x h  =  40 cm²

Here altitude (or) height = 15 cm

b x 15 = 40  ==> b = 2.67 cm

Example 4 :

Find the height of a parallelogram if its area is 612 cm² and its base is 18 cm.

Solution :

Area of a parallelogram  = 612 cm²

b x h = 612 cm²

base = 18 cm

18 x h  = 612 ==>  h =  34 cm

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