Area and Perimeter

Perimeter and area are the small things you learn that are great applications outside. Many things depend on measuring the perimeter and area. It is useful in designing pipes, microscopes, buildings, roads, and many such things. The Perimeter, area and volume of different shapes help us to extract complete information about the shape. In addition, perimeter and area help us to find the dimensions of any object. Learning about shapes, area and perimeter formulas can be of great help. They help in fields like physics, biology, and engineering. Perimeter and area form the core part of geometry.

What is Area and Perimeter of a Shape

1. What is the definition of perimeter?

The perimeter of any shape is the length of the boundary of the shape. It measures all the sides of the shape. You can find the perimeter simply by adding the length of the sides and edges of the shape. The unit used to measure the perimeter is a centimeter, meter, etc.

2. What is the definition of area?

The area is the plane enclosed by the perimeter and measures the extent of any shape. When you are measuring the area of 2D shapes it gives the value of the enclosed plane. And when you are talking about the area of the 3D shape, it gives the value of the border of the shape. The unit of area centimeter squared, meter squared, etc.

Area and Perimeter of Different Shapes

1. Square

A Square is a shape having all four sides equal. Any two adjacent sides of a square make an angle of 90 degrees with each other.

• The formula for the area of the square is given as below.

Area of square = (side)^{2}

• The perimeter of a square is given as below.

Perimeter of the square = 4*(side)

2. Rectangle

A rectangle is a quadrilateral which has opposite sides equal. For a rectangle, the adjacent sides make an angle of 90 degrees with each other. The variables 'l' and 'b' denote the values of the length and breadth of a rectangle.

• The formula for the area of a rectangle is given as below.

Area of a rectangle = l*b

• The formula of the perimeter of a rectangle is given as follows:

The perimeter of a rectangle = 2(l + b)

3. Circle

The circle is a shape with no edges. The distance of any point of the circle from its center is given by the radius of the circle. The perimeter of a circle is called by a special name, circumference of the circle. The variable 'r' denotes the radius of the circle.

• The formula for the area of a circle is given as below.

Area of a circle = \pi r^{2}

• The formula for the circumference of a circle is given as below.

Circumference of a circle = 2 \pi r

4. Triangle

Triangle is a shape having three sides. The sides of a triangle can have different lengths. The sum of the angles of the triangles should be 180°. To find the area of a triangle we need the values of the height and base of a triangle.

• The formula for the area of a triangle is given as below.

Area of a triangle = \frac{1}{2}*base* height

The formula for the perimeter of the triangle is given as below.

Perimeter of a triangle = sum of all sides

5. Rhombus

The rhombus is a quadrilateral having all sides equal. The angle between adjacent sides is not compulsory 90°. The opposite angles of the rhombus are the same. To find the area of the rhombus we need the value of its height and base.

• The formula for the area of a rhombus is given as below.

Area of a rhombus = base* height

• The formula for the perimeter of the rhombus is given as below.

The perimeter of a rhombus = 4*side

6. Parallelogram

A parallelogram is a shape having opposite sides parallel. To find the area of a parallelogram we need the value of its height and base.

• The formula for the area of a parallelogram is given as below.

Area of a parallelogram = base* height

• The formula of the perimeter of a parallelogram is given as below.

The perimeter of a rhombus = 2(sum of adjacent sides)

List of All Formula of Area and Perimeter and The Relation Between Them

Examples of Area and Perimeter

• What is the perimeter of a square having an area of 49 sq. cm?

The area of the square is 49 sq. cm. Using this information we will find the side of the square

Area = (side)^{2}

49 = (side)^{2}

Taking square root

side = 7 cm

Perimeter = 4*(side)

= 4*7

= 28 cm

• What is the area of the rhombus having a base and height of 7 and 8 m?

The formula of the area of rhombus is base * height

Area = base * height

= 7 * 8

= 56 sq.m

• Find the area of an equilateral triangle having a side perimeter of 9cm.

Area = \frac{\sqrt{3}}{4}(side)^{2}

The perimeter of the equilateral triangle = 3*(side)

9 = 3(side)

Side = 3

Area = \frac{\sqrt{3}}{4}(side)^{2} \\

Area = \frac{\sqrt{3}}{4}(3)^{2} \\

Area = \frac{9\sqrt{3}}{4}

• If the circumference of the circle is 12 \pi then find its radius.

Circumference of circle = 2 \pi r

12 \pi = 2 \pi r

r = 6

• If the diagonal of the rectangle is 5cm and one of its sides is 3 cm. Find the value of the perimeter of the given rectangle.

Adjacent sides of a rectangle make an angle of 90° with each other. Hence, the triangle is formed by a diagonal and the adjacent sides are a right-angled triangle.

We can use Pythagoras' theorem

(diagonal)^{2} = (side1)^{2} + (side2)^{2} \\

(5)^{2} = (3)^{2}+(side2)^{2} \\

25 - 9 = (side2)^{2} \\

16 = (side2)^{2} \\

side2 = 4

Perimeter = 2( sum of adjacent sides)

the first = 2(3 + 4)

= 14 cm