4 What Is Area ? Area is the amount of space inside a shape: Area Area 1cmArea is measured in square units.1cm2A square unit is a square measuring one unit in each direction. For example:It is written as :
5 Estimating The Area. B A C D Look at the four shapes below and use your judgement to order them from smallest to largest area:ABCD
6 B A C D To decide the order of areas consider the four shapes again: To measure the area we must determine how many square centimetres are in each shape:Each shape is covered by 36 squares measuring a centimetre by a centimetre .We can now see that all the areas are equal at 36cm2 each.
7 Area Of A Rectangle. C Length Width The formula for the area of a rectangle is:A = LWfor short.Area = Length x Widthor
8 We can now calculate the area of each rectangle very quickly: (1)(2)A= L x WA = 12 x 3 =36cm2(3)A= L x WA = 6 x 6 =36cm2A= L x WA= L x W(4)A = 18 x 2 =36cm2A = 9 x 4 =36cm2
9 Example 1Calculate the area of the rectangle below:(2)3m5m7cm4cm(1)SolutionThis area is in square metres:1mA = LWSolutionA = LWL = 7W = 4L = 3W = 5A = 7 x 4A = 3 x 5A = 28cm2A = 15m2
10 Example 3.Solution.8cm2cm5cm3cmSplit the shape up into two rectangles:A1Calculate the area of A1 and A2.A22A1A2356Calculate the area of the shape above:Area = A1 + A2Area = ( 2 x 5) + (6 x 3)Area =Area = 28cm2
11 What Goes In The Box ? Find the area of the shapes below : (1) 8cm 6cm (2)48cm2(3)17cm8cm12cm5cm11.34m2141cm2
12 The Area Of A Triangle. Consider the right angled triangle below: 5cm BaseHeightWhat shape is the triangle half of ?The formula for the area of a triangle is:RectangleArea = ½ x Base x HeightWhat is the area of the rectangle?A = ½ BHArea = BH
13 Does the formula apply to all triangles ? Base (B)Height (H)Can we make this triangle into a rectangle ?YesThe triangle is half the area of this rectangle:The areas marked A1 are equal.BHA1A2The areas marked A2 are equal.For all triangles:Area = ½ BH
14 Calculate the areas of the triangles below: Example 1Example 210cm6cm6.4m3.2mSolution.Solution.Area = ½ x base x heightArea = ½ x base x heightheight = 6cmbase = 10 cmheight = 3.2mbase = 6.4mArea = ½ x 10 x 6Area = ½ x 6.4 x 3.2Area = ½ x 60 = 30cm2Area = ½ x = 10.24m2
15 Example 3.Calculate the area of the shape below:Solution.16m12m10mDivide the shape into parts:A1A2Area = A1 + A2A1A210101216-12 =4Area = LW + 1/2 BHArea = 10 x ½ x 4 x 10Area =Area = 140m2
16 What Goes In The Box ? Find the area of the shapes below : (1) 8cm (2)10.2 m6.3m32.13m2(3)25m18m12m258m2
17 The Area Of A Parallelogram. A Parallelogram is any closed shape which has two sets of parallel sides.
18 We are now going to find a formula for the area of a parallelogram: Divide the shape into parts:hbArea = b x hHeight and Base have to be perpendicular
19 Example 1Calculate the area of the parallelogram below :Solution ( Using the formula).16cm13cmArea = b x hb = 16h =13Area = 16 x 13Area = 208 cm2