10.6.1 Areas of Rectangles

Activity Symbol Activity: Areas of Rectangles

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

Solution Symbol

Answer

(a) Area of rectangle equals length multiplication width

So, the area of the garden equals 10.5 m multiplication 14 .2 m equals 149 .1 m super two.

So, the area is about 150 square meters.

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

Hint symbol

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.

Solution Symbol

Answer

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

The area of the top rectangle = 10.15 m multiplication three .22 m equals 32 .683 m super two. The bottom rectangle has a width of 2.84 m. Its length = 7.52 m negative 3.22 m equals four .3 m. So, area of bottom rectangle = 4.3 m multiplication two .84 m equals 12 .212 m super two. We can add these values to get the total area. So total area = equation left hand side 32.683 times m super two plus 12.212 times m super two equals right hand side 44.895 times m super two.

So, the total area of the room is about 45 times m super two.

Activity Symbol 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?

Hint symbol

Comment

Sketch the rectangle showing the measurements.

Solution Symbol

Answer

(a) The area of the rectangle = 18 cm prefix multiplication of two cm equals 36 cm super two. The perimeter = 18 cm plus two cm plus 18 cm plus two cm equals 40 cm.

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

Hint symbol

Comment

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

Solution Symbol

Answer

(b) The area must be 36 times cm super two, 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 36 times cm super two, 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?

Hint symbol

Comment

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

Solution Symbol

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 19 times cm super two. Another rectangle would be one with sides of 19.5 cm and 0.5 cm that has an area of 9.75 times cm super two. Other combinations are possible.

Videoclip iconIf 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)] .

10.6.2 Formulas for Areas