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# Area and Perimeter Formula

Last updated date: 20th Sep 2024
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As we know that geometry is the study of shapes. Geometry deals with plane shapes and solid shapes. We calculate different terms associated with the shapes, like length, width, height, area, perimeter, volume, etc. Area and volume are the two important concepts used in our daily life. We come across many shapes whose required space and distance around them have to be calculated and this is termed as the area and perimeter of the shapes. We see many shapes around like squares, rectangles, circles, polygons, etc. Every shape has its unique properties and measurements. Hence every shape has a different area and perimeter, based on its measurements. So here on this page, we will study Maths area and perimeter formulas associated with different shapes.

### Area and Perimeter Definition

The area is the space occupied by any two-dimensional geometric figure and the perimeter is the distance around the shape or you can say boundary of the shape.

The ways to measure the area and perimeter are completely different.

### Area

The area is the measurement of the space occupied by any two-dimensional geometric shape. Or we can say, the quantity of space occupied by any shape, item, or flat surface is defined as the area of the shape, object, or flat surface. The actual area of a shape, an object, or a flat surface is defined by the total number of square units that can be included within it. Hence, the area of a shape is calculated in square units (sq units).

The area of any shape depends upon its dimensions. Different shapes have different areas. For instance, the area of the square differs from the area of the rectangle.

Eg.1.  Using a square grid paper, the concept of locating an area may be simply applied. The total number of unit squares included within a figure is equal to the figure's area in square metres.

Let's assume any blue square occupies 9 square units, which means that the square has a surface area of 9 square units.

Eg. 2. Suppose if you want to paint the rectangular wall of your house, you need to know the area of the wall to calculate the quantity of the paint required to paint the wall and the cost of painting.

If two figures have a similar shape it is not necessary that they have equal area unless and until their dimensions are equal. Suppose two squares have sides s and s1, so the areas of the two squares will be equal is s = s₁

There are many real-life examples also, such as:

• Utilisation of the concept of area to determine the amount of space that needs to be painted on a wall.

• The amount of space in a room's floor that needs to be covered with tiles.

• The amount of space in a backyard that needs to be planted with flowers, and so on.

### Perimeter

The word 'perimeter' is derived from the Greek word 'Perimetron.' “Peri” is a Latin word that means 'about,' and 'Metron' is a Greek word that means “measure.”

Adding up the lengths of all the sides of a form or measuring the outer limit of a shape or object, yields the perimeter of that shape or object. The perimeter is the length of the boundary enclosed by any geometric shape. The perimeter of the shape depends on the length of the shape.

For example, a metal wire of length 10cm can form both the circle and the square.

Suppose you have to fence your house, the length required for fencing is the perimeter of the house.

Perimeters of two shapes can be equal only if their length is equal.

Some real-world applications of the perimeter include:

• Determining the length around a photo frame.

• The length around a lawn for which a fence is required.

Finding the perimeters of small things can be accomplished by wrapping a string or thread around the object whose perimeter has to be determined.

For polygons, the perimeter is computed by summing the sides of the polygon and expressing them in the provided units.

Area and Perimeter Formulas For all Shapes

There are different types of shapes with different dimensions.  So their area and perimeter formulas also differ. Here are the different area and perimeter formulas for all shapes. Given below is the area and perimeter formula chart which will provide you with the area and perimeter formulas for all shapes.

Area and Perimeter Formula Chart

 Name of the Geometric Shapes Figure Area Formula Perimeter Formula Variables Rectangle (image will be uploaded soon) Area = l x w Perimeter = 2(l+w) L = lengthW = Width Square (image will be uploaded soon) Area = a2 Perimeter = 4a a = sides of the square Triangle (image will be uploaded soon) Area = ½ x b x h Perimeter = sum of all sides b = baseh = height Trapezoid (image will be uploaded soon) Area = ½ (a+b)h Perimeter = sum of all sides a = base1b = base2h = vertical height Parallelogram (image will be uploaded soon) Area = b x h Perimeter = 2(a+b) a = sideb = baseh = vertical height Rhombus (image will be uploaded soon) Area = a x h Perimeter = 4a a = side of the rhombush = height Circle (image will be uploaded soon) Area = πr2 Perimeter/circumference = 2πr r = radius of the circle= 22/7 or 3.1416 Semicircle (image will be uploaded soon) Area =½ πr2 Perimeter = πr + 2r r = radius of the circle

This area and perimeter formula chart will help you to memorize these formulas at a glance. Keep this area and formula chart handy with you always.

### Solved Examples

Here are some solved examples based on the area and perimeter formulas of different shapes.

Example 1: If the radius of a circle is given as 7cm. Find its area and circumference.

Solution: Given that radius = 7cm

We have, Area A = π × r2

A = 22/7 × 7 × 7

A = 154 cm2.

And Circumference, C = 2πr

C = 2 x 22/7 x 7

C  = 44 cm

Example 2: If the length of the side of a square is 9 cm. Then find its area and the total length of its boundary.

Solution: Given that length of the side of square, a = 9 cm

We have Area formula as A = a2

= (9)2

= 81 cm2

Total length of its boundary is the Perimeter of the square

We have perimeter = 4a

= 4 x 9

= 36cm.

Therefore, the area of the square is 81cm2 and the total length of its boundary is 36 cm.

Example 3: The length of the rectangular field is 15m and width is 6m. Find the area and perimeter of the field.

Solution: Given that,   Length = 15m

Width = 6m

We have,  Area formula A = length x width

= 15 x 6

= 90 m2

And Perimeter formula P = 2 (length + width)

= 2 x (15 + 6)

= 2 x 21

= 42 m.

### Quiz Time

Check your progress by solving some more problems in the area and perimeter of different shapes.

1. Find the cost of carpeting a room 13m long and 9m broad at the rate of 12.40 rs per metre.

2. The area of a square is 121sq.cm. Find its side.

### Conclusion:

Mathematical derivations and applications become hard to understand without the right guidance. You can refer to this article for a thorough understanding and better results.

## FAQs on Area and Perimeter Formula

1.What is the Difference Between Area and Perimeter?

Area is defined as the space occupied by the shape. While perimeter is defined as the distance around the shape(the boundary of the shape).

Shapes with the same area can have different perimeters and the shapes with the same perimeter can have different areas. The area is measured in square units and the perimeter is measured in linear units. The area can be measured for 2 - dimensional objects while the perimeter is measured for one-dimensional shapes.

The below figure represents the difference between area and perimeter.

2.How to measure the Area and Perimeter of irregular objects?

In an irregular shape, the lengths of the sides differ from one another. When calculating the area of these shapes, it is necessary to divide the shape down into common shapes such as squares, rectangles, triangles, and circles.

This is because each of these forms has a set formula for determining its area. The ability to recognise the shapes within shapes is essential when attempting to calculate the area of irregular shapes.

After you've calculated the area of each form, add them together to get the overall area. When calculating the perimeter of an irregular object, simply measure the length of each side and add the results together.

3.Are the terms volume and area same?

There are several applications of Area and Volume in daily life. But the terms "area" and "volume" are not the same. The two-dimensional surface measurement of an object is referred to as its area, whereas the three-dimensional spatial measurement of an object is referred to as its volume. Units of the area will always be squared, and units of volume will always be cubed.

Eg. In the case of a cup, if it can hold 100 ml of water up to the brim, its volume is expressed as 100 ml = 100 cubic centimetres. Whereas the area (here) concerns the surface area of the cup.