Calculate Area of Composite Shapes We are Learning to…… Calculate Area of Composite Shapes

Area of shapes made from rectangles How can we find the area of this shape? We can think of this shape as being made up of two rectangles. 7 m Either like this … A 10 m 15 m … or like this. 8 m Label the rectangles A and B. Discuss ways to divide this composite shape into rectangles. A third possibility not shown on this slide would be to take the square of area 15 m × 15 m and to subtract the area of the rectangle 10 m × 8 m. This gives us 225 m2 – 80 m2 = 145 m2. B 5 m Area A = 10 × 7 = 70 m2 15 m Area B = 5 × 15 = 75 m2 Total area = 70 + 75 = 145 m2

Area of shapes made from rectangles How can we find the area of the shaded shape? We can think of this shape as being made up of one rectangle cut out of another rectangle. 7 cm A 3 cm Label the rectangles A and B. 8 cm 4 cm B Area A = 7 × 8 = 56 cm2 Discuss ways to find the shaded area before revealing the solution. Area B = 3 × 4 = 12 cm2 Total area = 56 – 12 = 44 cm2

Area of an irregular shape on a pegboard How can we find the area of this irregular quadrilateral constructed on a pegboard? We can divide the shape into right-angled triangles and a square. A B Area A = ½ × 2 × 3 = 3 units2 Area B = ½ × 2 × 4 = 4 units2 Area C = ½ × 1 × 3 = 1.5 units2 Discuss how the area can be found using right-angled triangles and rectangles. D E Area D = ½ × 1 × 2 = 1 unit2 C Area E = 1 unit2 Total shaded area = 10.5 units2

Area of an irregular shapes on a pegboard How can we find the area of this irregular quadrilateral constructed on a pegboard? An alternative method would be to construct a rectangle that passes through each of the vertices. A B The area of this rectangle is 4 × 5 = 20 units2 D The area of the irregular quadrilateral is found by subtracting the area of each of these triangles. C

Area of an irregular shapes on a pegboard How can we find the area of this irregular quadrilateral constructed on a pegboard? Area A = ½ × 2 × 3 = 3 units2 A B Area B = ½ × 2 × 4 = 4 units2 Area C = ½ × 1 × 2 = 1 units2 Area D = ½ × 1 × 3 = 1.5 units2 Total shaded area = 9.5 units2 Area of irregular quadrilateral = (20 – 9.5) units2 C D = 10.5 units2

Area formulae of 2-D shapes You should know the following formulae: b h Area of a triangle = b x h 2 b h Area of a parallelogram = b x h l w Use this slide to summarize or review key formulae. Area of a rectangle = l x w

To succeed at this lesson today you need to… 1. Break the shape into either rectangles and/or triangles 2. Work out the area of each part 3. Find the total Complete Handouts 4.2.1 and 4.2.2