Finding the perimeter and area of rectangles and squares

Perimeter of rectangles and squares

Previously, we worked out what the perimeter of this rectangle was even though we were not given the length of all four sides. We used our knowledge of rectangles to do this.

The lengths of the opposite sides of a rectangle are always equal. Therefore, we know that that length of the other two sides are 5 cm and 8 cm. So the perimeter is 5 cm + 5 cm + 8 cm + 8 cm = 26 cm.

Answer: Well, we know that the perimeter of this rectangle is always going to be base + base + height + height. Why don't we just simplify this to (2 x base) + (2 x height) or 2 x (base + height).

The perimeter of a rectangle can be written as P = 2b + 2h.

Note: Sometimes we call the sides of a rectangle length (the longer sides) and breadth (the shorter sides). In this case we could say that P = 2l + 2b.

Question: Now work out a simple formula for the perimeter of any square. We will call the sides side.

Area of rectangles and squares

In the previous section, we saw that we can use shortcuts to find the perimeter of rectangles and squares because we know that the length of the opposite sides of a rectangle are always equal and the length of all four sides of a square are always equal.

• Perimeter of a rectangle = 2b + 2h (base and height) or P = 2l + 2b (length and breadth)
  
• Perimeter of a square = 4s
  

Now, let's think about the area of these shapes. We know that area is a measure of the number of square units inside a shape. Look at this rectangle again and count the number of square units inside it.

Did you get 40 square centimetres or 40 cm²? Can you see that there are eight rows of five squares (8 x 5) or five rows of eight squares (5 x 8)?

Question: Can you write a simple formula for the area of a rectangle? Remember, we can call the sides the base and height or the length and breadth.

Answer: The area of a rectangle is given as A = b x h (base and height) or A = l x b (length and breadth).

Question: Now work out a simple formula for the area of any square.

Activity: Perimeter and area of rectangles

If you need more help to find the perimeter and area of rectangles and squares, work through the CK-12 FlexBook chapter called Area and perimeter of Rectangles.

Activity: Interactive challenge

Work through this interactive challenge from CK-12 to practice finding the perimeter and area of rectangles and squares.

Exercise: Challenge question

Raj has a small patch of land that he wants to turn into a vegetable garden. However, he wants to build a fence around it before he plants anything. He knows that the area of the land is 240 m² and that the length of one side is 1 m longer than the other side.

1. What is the perimeter of the vegetable garden?
   
2. If the wood for the fence comes in 2.5 m lengths, how many lengths will Raj need to buy?