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We use the terms area and perimeter quite often in the classroom. We also know that area and perimeter are characteristics related to geometrical shapes. As we go further, we will learn the difference between area and perimeter and the steps involved in calculating area and perimeter....Read MoreRead Less

Area and perimeter are two important properties of two-dimensional shapes. We use the concept of area and perimeter to describe the size of shapes. In general, small shapes will have a smaller area and perimeter. On the other hand, bigger shapes will cover a larger area and will have a longer perimeter. But in some cases, the shape can have a long boundary, and a smaller area at the same time. We will look into the concept of area and perimeter for different shapes.

Area is the extent of the region occupied by a shape on a plane. We generally relate the size of a shape with its area. We use the concept of area to compare the size of two pieces of land. Similarly, we use the concept of area to measure the size of a wall, to paint it or to apply some wallpaper to the wall.

Perimeter is the length of the boundary of a shape. In other words, the perimeter of a shape is the sum of the length of its sides. For example, we usually use the concept of perimeter to measure the length of the wall around a piece of land. We use the same concept to measure the length of the border of a country.

Even though area and perimeter are used to describe the size of a shape, they are entirely different concepts. The units used for measuring both of these quantities are different. We measure perimeter using units like inches, feet, miles, centimeters, meters and so on. These are the same units that we use for measuring the length of a side. Since perimeter is the sum of the length of the sides of a shape, the unit remains the same. On the other hand, the units of area are the square of the units we use to measure the perimeter, and are written as, square inches, square feet, square miles, square centimeters, square meters and so on.

We use the concept of area and perimeter for different purposes. For example, we use the concept of area to find the area of a farm, and we use the concept of perimeter to find the length of the fencing around it.

Shape | Area | Perimeter |

Square | \(a^2\) | 4a |

Rectangle | \(l~\times~b\) | \(2~\times~(l~+~b)\) |

Triangle | \(\frac{1}{2}~\times~b~\times~h\) | \((a~+~b~+~c)\) |

Rhombus | \(\frac{1}{2}~\times~d_1~\times~d_2\) | 4a |

Trapezoid | \(\frac{1}{2}~\times~h(b_1~+~b_2)\) | Sum of all sides |

**Example 1:** **Find the area of the square. **

**Solution: **

Length of the sides of the square, a = 4 inch

Area of the square = \(a^2 \)

= \(4~\times~4\)

= 16 square inches

Perimeter of the square = 4a

= \(4~\times~4\)

= 16 inches

So, the area of the square is 16 square inches, and its perimeter is 16 inches.

**Example 2: ****What is the area and perimeter of the rectangle given below?**

**Solution: **

l = 12 ft

b = 4 ft

Area of rectangle = l \(\times\) b

= 12 \(\times\) 4

Area of rectangle = 48 square feet

Perimeter of rectangle = 2 \(\times\) (l + b)

= 2 \(\times\) (12 + 4)

= 2 \(\times\) 16

Perimeter of rectangle = 32 feet

Therefore, the area of the rectangle is 48 square feet, and its perimeter is 32 feet.

**Example 3:** **Find the area and perimeter of the triangle.**

**Solution:**

h = 3 inches

b = 8 inches

a = c = 5 inches

Area of the triangle = \(\frac{1}{2}~\times~b~\times~h\)

= \(\frac{1}{2}~\times~8~\times~3\)

= \(4~\times~3\)

= 12 square inches

Perimeter of the triangle = a + b + c

= 5 + 8 + 5

= 18 inches

The area of the square is 12 square inches, and its perimeter is 18 inches.

Frequently Asked Questions

The perimeter of a shape is the length of its boundary, and its area is the space enclosed by the boundary.

Even though there is no direct relationship between the area and perimeter of a geometrical shape, we can say that the area of a regular shape increases with the ** increase** in perimeter.

Square inches, square feet, square miles, square centimeters, square meters and square kilometers are some examples of the units used to represent the area of a shape.

The unit of perimeter is the same as that of length. We use units like inches, feet, miles, centimeters, meters and kilometers to measure the perimeter of shapes.