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© Boardworks Ltd 2004 1 of 84 KS3 Mathematics S8 Perimeter, area and volume

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© Boardworks Ltd 2004 2 of 84 A A A A A A Contents S8 Perimeter, area and volume S8.1 Perimeter S8.6 Area of a circle S8.2 Area S8.5 Circumference of a circle S8.3 Surface area S8.4 Volume

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© Boardworks Ltd 2004 3 of 84 Put these shapes in order

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© Boardworks Ltd 2004 4 of 84 Perimeter To find the perimeter of a shape we add together the length of all the sides. What is the perimeter of this shape? 1 cm 3 3 2 1 1 2 Perimeter = 3 + 3 + 2 + 1 + 1 + 2 = 12 cm Starting point

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© Boardworks Ltd 2004 5 of 84 Perimeter of a rectangle To calculate the perimeter of a rectangle we can use a formula. length, l width, w Using l for length and w for width, Perimeter of a rectangle = l + w + l + w = 2 l + 2 w or = 2( l + w )

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© Boardworks Ltd 2004 6 of 84 Perimeter What is the perimeter of this shape? b cm a cm 9 cm 5 cm 12 cm 4 cm The lengths of two of the sides are not given so we have to work them out before we can find the perimeter. Let’s call the lengths a and b. Sometimes we are not given the lengths of all the sides. We have to work them out using the information we are given. For example,

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© Boardworks Ltd 2004 7 of 84 Perimeter 9 cm 5 cm b cm 12 cm a cm 4 cm a = 12 – 5 cm = 7 cm 7 cm b = 9 – 4 cm = 5 cm 5 cm P = 9 + 5 + 4 + 7 + 5 + 12 = 42 cm Sometime we are not given the lengths of all the sides. We have to work them out from the information we are given.

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© Boardworks Ltd 2004 8 of 84 Calculate the lengths of the missing sides to find the perimeter. P = 5 + 2 + 1.5 + 6 + 4 + 2 + 10 + 2 + 4 + 6 + 1.5 + 2 Perimeter 5 cm 2 cm 6 cm 4 cm 2 cm p qr s t u p =2 cm q = r =1.5 cm s =6 cm t =2 cm u =10 cm = 46 cm

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© Boardworks Ltd 2004 9 of 84 P = 5 + 4 + 4 + 5 + 4 + 4 Perimeter What is the perimeter of this shape? Remember, the dashes indicate the sides that are the same length. 5 cm 4 cm = 26 cm

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© Boardworks Ltd 2004 10 of 84 Perimeter Perimeter = 4.5 + 2 + 1 + 2 + 1 + 2 + 4.5 Start by finding the lengths of all the sides. 5 m 2 m 4 m 4.5 m 4.5 cm 1 cm = 17 cm What is the perimeter of this shape?

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© Boardworks Ltd 2004 11 of 84 Before we can find the perimeter we must convert all the lengths to the same units. Perimeter 3 m 2.4 m 1.9 m 256 cm In this example, we can either use metres or centimetres. Using centimetres, 300 cm 240 cm 190 cm P = 256 + 190 + 240 + 300 = 986 cm What is the perimeter of this shape?

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© Boardworks Ltd 2004 12 of 84 Equal perimeters Which shape has a different perimeter from the first shape? A B C A B C A BC B A A

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