# 10.6.1 Areas of Rectangles

## Activity: Areas of Rectangles

(a) A rectangular garden is 10.5 m long and 14.2 m wide. What is its area?

### Answer

(a)

So, the area of the garden .

So, the area is about 150 square meters.

(b) What is the floor area of this L-shaped room?

### Comment

Calculate the length of the smaller rectangle using the width of the larger one and the full length of the left hand side of the room.

### Answer

(b) The area of the room can be calculated by adding the areas of the rectangles.

The area of the top rectangle = . The bottom rectangle has a width of 2.84 m. Its length = . So, area of bottom rectangle = . We can add these values to get the total area. So total area = .

So, the total area of the room is about .

## Activity: Areas and Perimeters

Imagine a rectangle that is 18 cm long and 2 cm wide.

(a) What is the area of the rectangle? What is its perimeter?

### Comment

Sketch the rectangle showing the measurements.

### Answer

(a) The area of the rectangle = . The perimeter = .

(b) Can you draw another rectangle that has the same area but a smaller perimeter? What is the smallest perimeter you can make?

### Comment

Think about pairs of factors of 36 (that is pairs of numbers that when multiplied together give 36).

### Answer

(b) The area must be , and the perimeter must be less than 40 cm. This means that we want to find two numbers which multiply together to give 36, and which add together to give a number less than 20. There are many possibilities.

For example, a rectangle that is 9 cm by 4 cm has an area of , but its perimeter is only 26 cm. Similarly, a rectangle with sides 10 cm and 3.6 cm has the same area but a perimeter of 27.2 cm. The smallest perimeter (24 cm) is for a square of side 6 cm.

(c) Can you draw another rectangle that has the same perimeter as in part (a) but a smaller area?

### Comment

Look again at the answer to part (b) to see if this can help you.

### Answer

(c) Here we need to find two numbers which add up to 20 cm (width + length) but whose product is less than 36. A rectangle with sides of 19 cm and 1 cm has a perimeter of 40 cm but an area of only . Another rectangle would be one with sides of 19.5 cm and 0.5 cm that has an area of . Other combinations are possible.

If you want some more practice with areas and perimeters of rectangles that will also help you to brush up on your multiplications tables have a quick go at this game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

10.6 Areas