Area and volume. 6.1 Area of a triangle. 1 Calculate the areas of the following triangles.
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1 6 Area and volume 6.1 Area of a triangle 1 Calculate the areas of the following triangles. 9 cm 16 m 23 mm 9 m 30 mm 8 cm 6 mm 24 mm 11 cm 20 mm 2 Copy and complete the table below which gives the measurements of five triangles. Base Height Area 12 cm 9 cm 8 cm 14 cm 6 mm 7 mm 1 64 cm 2 20 m 100 m Area of a triangle NMF Homework Book 2_CH6.indd 37 19/03/14 1:29 PM
2 3 Use squared paper to draw four different triangles with area 24 cm2. (Hint: Draw the base first, using a whole number of centimetres that is a factor of 48, for example, 8 cm. Then calculate the height of the triangle.) 4 Calculate the height of each triangle below using the area given. 12 cm Area = 10 m 2 Area = 3 2 Area = 4.5 m 2 5 Each puzzle piece below is a compound shape, and can be put together to make a complete shape. Each small square represents a square centimetre. How much area will the completed puzzle cover? y A B C O x G F E D 6 Work out the area of the shapes below. 2 cm 19 cm 4 cm 4 cm 10 cm 12 cm 38 6 Area and volume NMF Homework Book 2_CH6.indd 38 19/03/14 1:29 PM
3 R 7 The shapes below both have an area of 120 cm2. a In the two rectangles, the largest is 8 cm high, so how high is the smaller one? b If the base (dotted line) of the triangles measures 5 cm, what is the area of each triangle? c What must the height of each triangle be? 2 rectangles 2 triangles and 1 rectangle 10 cm 8 cm Area of a parallelogram 1 Calculate the areas of the following parallelograms. 5 mm 22 cm 8 mm 1 3 m 5 m 5.5 cm 2.5 cm 2 Copy and complete the table below which gives the measurements of five parallelograms. Base Height Area 7 cm 13 cm 9 m 19 m 250 mm 70 mm 15 m 120 m 2 12 cm 30 cm Area of a parallelogram NMF Homework Book 2_CH6.indd 39 19/03/14 1:29 PM
4 3 Use squared paper to draw four different parallelograms with area 48 cm2. (Hint: Draw the base first, using a whole number of centimetres that is a factor of 48, for example, 8 cm. Then calculate the height of the parallelogram.) 4 Find the area of each puzzle piece. Each piece is a compound shape or a parallelogram. Each small square represents a square centimetre. Show your calculations. A B C E D F G H I J K 5 Calculate the height of each parallelogram below using the area given. 26 mm 0.5 m 25 mm Area = 260 mm 2 Area = 4 m 2 Area = 150 mm 2 6 Work out a the perimeter and b the area of this parallelogram. 8.5 cm 7.5 cm 5 cm 7 Work out the value of h in this diagram. 4 cm h 3 cm 12 cm 40 6 Area and volume NMF Homework Book 2_CH6.indd 40 19/03/14 1:29 PM
5 Brainteaser The rhombus shown has an area of 24 cm 2. There are five possible whole number values of a and b; can you find them all? B a A b D C 6.3 Area of a trapezium 1 Calculate the areas of the trapezia below. 7 cm 20 mm 5 cm 10 mm 9 cm 1m 5 cm 4 cm 7 cm 100 mm 45 mm 8 cm 40 mm 80 mm 2 Copy and complete the table below for trapezia a through e. Trapezium Parallel side a Parallel side b Height h Area a 7 cm 9 cm 3 cm b 13 m 8 m 5 m c m 6 mm 3m 2 d 4 m 6 m 60 m 2 e 12 cm 10 cm 250 cm Area of a trapezium NMF Homework Book 2_CH6.indd 41 19/03/14 1:29 PM
6 3 Use squared paper to draw four different trapezia with area 24 cm2. (Hint: Decide the lengths of the parallel lines first and make sure that their total length is a factor of 48. For example, parallel sides 7 cm and 5 cm have a total length of 12 cm, which is a factor of 48. Then calculate the height of the trapezium.) 4 Find the area of each puzzle piece. Each piece is a compound shape or a trapezium. Each small square represents a square centimetre. Show your calculations. A B C D E F G H I 5 Work out the height, h, of the trapezium below if it has an area of: a 110 cm 2 b 75cm 2 7 cm h 13 cm 6 The area of this trapezium is 9 cm 2. Work out three different whole number values of a, b and h, with b > a. a h b 42 6 Area and volume NMF Homework Book 2_CH6.indd 42 19/03/14 1:29 PM
7 6.4 Surface area of cubes and cuboids 1 Find the surface area of each of the following cuboids. i ii 20 cm 4 m 5 m iii 12 cm 14 cm 2 cm 3 cm 27 cm 2 Calculate the surface area of a cube of side. 3 If a cube has a surface area of 150 cm2, what is the length of each side? 4 Krispies are sold in three sizes: mini, medium and giant. 120 mm 3 45 cm a b c 80 mm 24 cm 30 mm 12 cm Calculate the surface area of each box. (Hint: Convert mm to cm.) 3 24 cm How many times more cardboard is needed to manufacture the medium box compared to the small box (to the nearest whole number)? Do the same for the giant to the medium, to one decimal place. The area of the logo on the packet front of each box is as shown below: small box 40 cm edium box 448 cm 2 lgiant box 900 cm 2 Work out the fraction taken up by the logo each time in its simplest form. 6.4 Surface area of cubes and cuboids NMF Homework Book 2_CH6.indd 43 19/03/14 1:29 PM
8 5 Calculate the surface area of each of the following 3-D shapes. 3 cm 5 mm 8 cm 120 mm 10 mm 15 cm 10 cm 5 mm 50 mm 15 mm FS Brainteaser A scout group construct a wooden log store on a concrete base to keep their wood supply dry. The storage is a cuboid shape, 2.5 m long, wide and 1 m high with a hinged lid. To keep it waterproof it has to be coated in woodstain. a What area of wood has to be covered with i 1 coat? ii 2 coats? Water- based woodstain can be bought at for 2.5 litres. It claims to cover 8 m2 per litre and recommends applying two coats. b Oil- based tins cost for 2.5 litres, can cover 20 m2 but only needs one coat. c How much area can the water- based tin cover in total? How many tins are needed? d How much will be left over from these tins after two c oats are applied? e How many square metres does the oil- based tin cover per litre? f Which tin works out cheapest and by how much per litre? 44 6 Area and volume NMF Homework Book 2_CH6.indd 44 19/03/14 1:29 PM
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