Area and Perimeter

Key Concepts

• Perimeter and Area
• More Perimeter

19.4 Perimeter and Area 

Perimeter: 

The perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape. 

The rectangle on the geoboard 

How to find the perimeter and the area of a rectangle? 

To find the perimeter of the above fig. 1, we have to find the length of each side of the rectangle in centimetres and add them. 

3 + 2 + 3 + 2 = 10 

So, the perimeter of the rectangle is 10 centimetres. 

The area of the rectangle is 6 square centimetres. 

We can also measure the perimeter in inches and feet 

From the above fig 2,  

The perimeter is 12 inches and the area is 5 square inches. 

• The perimeter can be measured in centimetres (cm), inches (in), metres (m) and feet (ft). 
• The area can measure in square centimetres (cm²), square inches (in²), square metres (m²) and square feet (ft²). 

Real-life Examples: 

We often find the perimeter when putting up Christmas lights around the house or fencing the backyard garden. 

Example 1: 

The perimeter of all polygons can be determined by adding the lengths of their sides or edges. 

Regular Polygons	Irregular Polygons
Perimeter = 4 + 4 + 4 + 4                = 16 cm                OR Perimeter of regular polygons = number of sides x length of one side = 4 x 4  = 16	Perimeter of irregular polygons = 5 + 3 + 2 + 4 + 3 + 7 = 24 cm

19.5 More Perimeter 

Example 1: 

While making a card for your parents, you want to put yarn around the card. Measure the sides to find out how much yarn is required. 

The length and the width of the card are 6 inches and 4 inches, respectively. 

Given measurements are, 

6 + 4 + 4 + 6 = 20 

So, 20 inches of yarn is required for the card. 

Example 2: 

Find the perimeter of the following figure 

Perimeter = 3 + 2 + 3 + 3 + 2 

       = 13 square inches 

Example 3: 

The width of a rug is 14 feet. Its length is twice its width. What is the perimeter of the rug? 

Given width = 14 ft 

Length = 2 × w 

Length = 2 × 14 = 28 ft 

Perimeter = 14 + 28 + 14 + 28 = 84 ft 

∴The perimeter of the rug is 84 feet. 

What Have We Learned

• Understand the meaning of perimeter
• Compare the area and perimeter of two figures
• Find the area of figures to solve real-world problems
• Choose the appropriate tool and units of length to measure the perimeter
• Measure the perimeter of surfaces of objects and places
• Find the perimeter of a figure by adding up all its sides

Exercise:

1. A rectangular window has a length of 7 centimetres and a width of 4 centimetres. Find the perimeter of the rectangular window.

2. If the perimeter of a square piece of plywood is 140 inches, what is the length of each side?

3. What is the perimeter of the given figure? 7 in. 3 in.

4. A square has a width of 7 inches. What is the perimeter?

5. The perimeter of a square is 8 inches total. How long is each side?

6. If John made a garden that was 8 feet by 8 feet square, what is the perimeter of his garden?

7. What is the perimeter of a regular hexagon with a side that measures 7 centimeters?

8. What is the perimeter of a rectangle that is 6 inches long and 2 inches wide?

9. What is the perimeter of a regular hexagon with a side of 7 feet?

10. Wade built a fence around a rectangular section of his backyard. The length of the section is 20 feet and the width is 5 feet. What is the perimeter of the fenced section?

Concept Map: 

The perimeter of different shapes formulas: