3 Work out the length of the missing side in each right-angled triangle. The first one has been started for you. a b c Q3 hint Follow the steps in Q2. 7.2 cm 11 cm 8 cm 159 mm 13 cm 134 mm a c2 = a2 + b2 112 = a2 + 82 112 − 82 = a2 4 Work out the area of each shape. a b 7 cm Q4 hint c x x 13 cm 4 cm 8 cm x Sketch each right-angled triangle and label the sides. Use Pythagoras’ theorem to first find the length labelled x. Work out the area of the shape. 12 cm Enrichment 1 The diagram shows a smaller square inside a larger square. a Find the area of the smaller square. Try the two methods below. 4 cm 3 cm 3 cm x Method A Work out 4 cm 1 the length of one side of the larger square 2 the area of the larger square 3 the area of one triangle x 4 cm 4 the area of the smaller square, using your answers to steps 2 and 3. Method B Work out 3 cm 3 cm 4 cm 1 the length of x, using Pythagoras’ theorem. 2 the area of the smaller square, using your answer to step 1. 2 Reflect In these lessons you used these formulae: Circumference = p × diameter Area of a circle = p × radius2 Volume of a prism = area of cross-section x length Pythagoras’ theorem c2 = a2 + b2 Which formula was easiest to use? Explain. Which formula was most difficult to use? Explain. Discuss the formula you found most difficult with a classmate. Ask them to explain to you a question they answered using this formula. Q1b hint ‘Explain’ means write a sentence that begins, for example, ‘Method u, because __________.’ Reflect b Which method for working out the area of the smaller square did you prefer? Explain your answer. Unit 3 2D shapes and 3D solids 68