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?
So, the area of the garden .
So, the area is about 150 square meters.
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.
(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?
Sketch the rectangle showing the measurements.
(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?
Think about pairs of factors of 36 (that is pairs of numbers that when multiplied together give 36).
(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?
Look again at the answer to part (b) to see if this can help you.
(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 .