Composite Areas Teacher Extraordinaire will Mr. Peter Richard Teacher Extraordinaire will Show you how to compose yourself! Area of a rectangle Area of a triangle Area of Circles Area of composite shapes

Solution. Example 3. 8cm 2cm 5cm 3cm Split the shape up into two rectangles: A1 Calculate the area of A1 and A2. A2 2 A1 A2 3 5 6 Calculate the area of the shape above: Area = A1 + A2 Area = ( 2 x 5) + (6 x 3) Area = 10 + 18 Area = 28cm2

Example 3. Calculate the area of the shape below: Solution. 16m 12m 10m Divide the shape into parts: A1 A2 Area = A1 + A2 A1 A2 10 10 12 16-12 =4 Area = LB + 1/2 BH Area = 10 x 12 + ½ x 4 x 10 Area = 120 + 20 Area = 140m2

We are now going to find a formula for the area of the trapezium: b h Area = A1 + ( A2 + A3 ) Area = b x h + ½ x (a - b) x h Area = bh + ½ h(a - b) Divide the shape into parts: Area = bh + ½ ah – ½ bh A2 A1 A3 Area = ½ ah + ½ bh Work out the dimensions of the shapes: Area = ½ h ( a + b ) b A2 A3 A1 h Often common sense is as good as the formula to work out the area of a trapezium. h a – b

Example 2 Divide the shape into parts: 8m 14m 10m Area = rectangle + triangle Area = LB + ½ B H A = ( 10 x 8 ) + ( ½ x 6 x 10 ) A = 80 + 30 A = 110 m 2 10 10 14 – 8 = 6 8

Composite shapes 10 cm 6 cm ? ? 3 cm 13 cm

Composite shapes Area (1) = l x w = 10 x 6 = 60 cm² Area (2) ? (2) 3 cm Area (1) = l x w = 10 x 6 = 60 cm² Area (2) = ½ x b x h = ½ x 3 x 6 = 9 cm² Area of shape = (1) + (2) = 60 + 9 = 69 cm²

Example 4 Example 3 12cm 7cm A1 A2 7cm Split the shape into two areas. Find half the area of a circle: Area = A1 + A2 A =  r 2 2 Area = LB + ½  r 2. L = 12 B = 7 r = 3.5 A = 3.14 x 7 x 7 2 A = 12 x 7 + ½ x 3.14 x 3.5 x 3.5 A = 84 + 19.23 A = 76.93cm2 A = 103.2cm 2. (to 1 d.p)

Composite shapes Quiz and Homework! Quiz: Worksheet Page 249 Show all Work! Slime Work!