Area is the amount of space a shape covers. It is a 2D measurement. We measure area in square units. For small areas we use square centimetres.

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1 Area square units Area is the amount of space a spe covers. It is a 2D measurement. We measure area in square units. For small areas we use square centimetres. 1 Wt is the area of each sded spe? Each square s an area of ². a b c d e f 2 How many different spes can you make tt ve an area of 6 cm²? Do you need to use whole squares? How could you make an area of 6 cm² using part squares? Choose another area and see how many of those spes you can make. 16 Copyright P Learning

2 Area square units For larger areas such as a tennis court we use square metres (m²) For even larger areas such as countries, we use square kilometres. A square kilometre is m². 1 km 1 km How much space do you predict ² would take up? a Work in a small group and use clk or string to mark your prediction on the ground. Use a ruler to measure it out. Is it smaller or larger tn you imagined? b Now, how many people do you think could fit in your square? They must all be able to stand with both feet on the ground and inside the lines. Test it out. Record your prediction and the result. Estimate = Measurement = We also use hectares () to measure area. These are larger tn square metres but smaller tn square kilometres. We use them for measuring spaces such as farms or parks. 100 m 100 m 100 m 100 m = m² = 1 4 Convert the following: a m² b m² c m² d m² e m² f m² g 4 m 2 h 9 m 2 i 12 m 2 j m² k m² l m² 5 Would you choose cm², m², or km² to measure the area of the following? a This page b Egypt c A farm d A mobile phone screen e A city park f A national park g A DVD cover h A football stadium Copyright P Learning 17

3 Area find area using formulae We can use this formula to find the area of rectangles. Area = Length Width Area = 4 cm 2 cm = 8 cm² 4 cm 2 cm 1 Use the formula A = L W to help you find the areas* of: a b c This saves us from ruling up grids and counting squares. 2 m m m 4 cm m A = A = A = *Not drawn to scale. 2 Find the area of the following: a A rectangle measuring 8 cm 5 cm b A box measuring 0 cm 7 cm c A pool measuring 25 m 10 m d A phone measuring 4.5 cm 10 cm e A book measuring 5 cm 12 cm f A field measuring 60 m 25 m g A town square with 4 sides of 10 m h A rug measuring 10.2 m.4 m Answer these area word problems: a Marianne wants to buy new carpet for her bedroom. Her room is m 4 m and the carpet she wants costs $50 per m². How much will the new carpet cost her? b A book is 12 cm longer tn it is wide. If it is 10 cm wide, wt is the area of the book? c A garden s an area of 5 m². If the garden is 7 m long, wt is its width? d The area of a rectangle is 48 cm². Wt might be the length and width? Come up with 2 options: Option 1 L = W = Option 2 L = W = 18 Copyright P Learning

4 Area find area using formulae Each triangle is lf of a rectangle. To find the area of a triangle, we find the area of the rectangle and then divide by two. Rectangle = 8 cm 4 cm = 2 cm² Triangle = 2 cm² 2 = 16 cm² The formula for this is: 1 2 Base Height 4 Find the area of the sded triangles inside the rectangles*: 4 cm 2 cm 10 cm a b c Area = m 2 6 cm This works for all triangles right angled, isosceles, equilateral and scalene. One formula fits all! cm 4 cm 5 cm d e *Not drawn to scale. 5 Find the area of these triangles* using the formula 1 2 Base Height: 6 cm 4 m 6 m cm 9 m 8 m a b Area = m 2 c Area = m 2 d A triangle with a base of 12 cm and height of 7 cm e A triangle with a base of 17 m and a height of 14 m f A triangle with a base of 10.2 m and a height of 9 m *Not drawn to scale. Copyright P Learning 19

5 Area find area of irregular and composite spes Not all spes are regular triangles or rectangles. We ve to find ways to measure the areas of composite and other irregular spes as well. One way is to break the spe into known spes, find these areas, and then add them together. 1 Find the area of these irregular spes*: 5 m 70 m 1 2 m 40 m 20 m 6 cm 6 cm cm 8 m 0 m a b c 6 cm 5 cm 5 cm 2 m 10 cm 8 cm 5 m 10 cm 8 cm d e f *Not drawn to scale. 2 Construct your own composite spe with an area of 20 cm². Label the lengths of the sides. 20 Copyright P Learning

6 Area find area of irregular and composite spes There is no exact way to find the area of some irregular spes. We can use grids to estimate. The smaller the squares on the grid, the closer the estimate. Estimate the area of these spes: a A = cm² b A = cm² c A = cm² You could mark the whole squares one colour, then match part squares with another. d A = cm² e A = cm² 4 On the grid on the right, draw an irregular spe for each area amount: a 800 m 2 b m 2 c m 2 10 m 10 m Copyright P Learning 21

7 Area area and perimeter Do spes with the same area ve the same perimeter? 4 cm² 4 cm² 1 Draw some spes with an area of 12 cm². Measure and record their perimeters in the table below. Wt do you find? Length Width Area 2 This time, use a perimeter of 20 cm as your starting point. Create different spes with a perimeter of 20 cm and calculate their area. 22 Copyright P Learning

8 Area area and perimeter Solve these problems. Show your working out: a The perimeter of a square is 48 cm. Wt is its area? b The perimeter of a rectangle is 0 cm. If the rectangle is 4 times as long as it is wide, wt is the area of the rectangle? c The area of a square is 6 m². Wt is its perimeter? 4 The desks in your classroom are long and 50 cm wide and seat 2 students. Your teacher would like you to put them in groups of so tt 6 students can sit comfortably. Draw at least 2 different options and calculate the perimeter and area of each option. Which is your preferred option? Why? Copyright P Learning 2

9 Area and perimeter puzzles solve Wt to do Skira s d it with her brothers wrecking her stuff and decides to fence off her own area of the family room using the sofa cushions. There are 8 cushions, each 50 cm long. If she uses two of the walls as part of her boundary, wt is the largest area she can make for herself tt is brother-free? Show her best option below: The garden path on the left is made up of 9 identical squares. a If the perimeter of the path is 20 m, wt is its area? b Wt about if the perimeter was 60 m? Wt would then be the area? c If the area of the path is 6 m², wt is its perimeter? How many steps are involved in this problem? Maybe I need to work out the area of each wall first. Paige wants to paint the walls of her room purple. Her parents say she can do it but only if the paint costs less tn $250. Paige s found some purple paint going cheap at $55 per 4 litre pot. Each pot will cover 9 m². Her bedroom is m 4 m and each wall is 2.5 m high. She s one window with an area of ² tt doesn t need to be painted. The ceiling is covered in silver stars already so she won t paint tt either. Can she do it? Show your working out. 24 Copyright P Learning

10 Animal rescue investigate Getting ready Four African animals ve been stolen by smugglers. Fortunately you intercepted them and can return the animals to their natural bitat. You ve four enclosures in which to transport the animals safely. You know the areas of each side of the box but you don t know the lengths, heights or widths. You need to select the right one for each animal. Wt to do Follow these directions: 1 Look at the approximate dimensions of the animals. 2 Now look at the boxes. The area of each side is specified. Knowing this, wt could the height, length and width of each side be? Label them. Join the animal to the box you think would fit it best. Guess, check and improve would be a useful strategy here. 2² 14 m² 6 m² 2 m² Giraffe H 5 m L 4 m W 4 m² 1.5 m² m² Elepnt H m L 7 m W 2 m 6 m² 6 m² 4 m² Hippo H m L 2 m 20 m² 5 m² W 2 m Lion H 1.5 m L W 2 m Copyright P Learning 25