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Area Of Shapes. 2cm 12m 5cm A1 10m A2 3cm 16m 8cm 7cm A1 A2 12cm What Is Area ? Area is the amount of space inside a shape: Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area Area is measured in square centimetres. 1cm2 1cm A square centimetre is a square measuring one centimetre in each direction. 1cm It is written as : 1cm2 Estimating The Area. Look at the four shapes below and use your judgement to order them from smallest to largest area: B A C D To decide the order of areas consider the four shapes again: B A C D 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. Area Of A Rectangle. Look again at one of the shapes whose area we estimated: C Breadth Length What was the length of the rectangle ? 9cm How many rows of 9 squares can the breadth hold ? 4 We can now see that the area of the rectangle is given by 9 x 4. The formula for the area of a rectangle is: Area = Length x Breadth or A = LB for short. We can now calculate the area of each rectangle very quickly: (1) (2) A= L x B A = 12 x 3 =36cm2 A= L x B (3) A = 6 x 6 =36cm2 (4) A= L x B A= L x B A = 18 x 2 =36cm2 A = 9 x 4 =36cm2 Example 1 Calculate the area of the rectangle below: (1) (2) 4cm 5m 7cm 3m Solution This area is in square metres: 1m A = LB Solution 1m A = LB L= 7 B=4 L= 3 B=5 A= 7 x 4 A= 3 x 5 A = 28cm2 A = 15m2 Example 3. Solution. 2cm Split the shape up into two rectangles: Calculate the area of A1 and A2. 5cm A1 2 A2 3cm A2 3 5 A1 8cm Calculate the area of the shape above: 6 Area = A1 + A2 Area = ( 2 x 5) + (6 x 3) Area = 10 + 18 Area = 28cm2 What Goes In The Box ? Find the area of the shapes below : (1) (2) 6cm 2.7m 8cm 4.2m 48cm2 17cm 11.34m2 (3) 5cm 12cm 141cm2 8cm The Area Of A Triangle. Consider the right angled triangle below: What is the area of the triangle ? Area = ½ x 40 = 20cm2 5cm Height 8 cm Base What shape is the triangle half of ? The formula for the area of a triangle is: Rectangle What is the area of the rectangle? Area = ½ x Base x Height A = ½ BH Area = 8 x 5 = 40 cm2 Does the formula apply to all triangles ? Height (H) Base (B) Can we make this triangle into a rectangle ? Yes The triangle is half the area of this rectangle: The areas marked A1 are equal. A1 A2 The areas marked A2 are equal. H A1 A2 For all triangles: B Area = ½ BH Calculate the areas of the triangles below: Example 1 Example 2 6cm 3.2m 10cm 6.4m Solution. Solution. Area = ½ x base x height Area = ½ x base x height base = 10 cm height = 6cm base = 6.4m height = 3.2m Area = ½ x 10 x 6 Area = ½ x 6.4 x 3.2 Area = ½ x 60 = 30cm2 Area = ½ x 20.48 = 10.24m2 Example 3. Calculate the area of the shape below: Solution. 12m Divide the shape into parts: Area = A1 + A2 10m A1 A2 16m 10 A1 10 A2 12 16-12 =4 Area = LB + 1/2 BH Area = 10 x 12 + ½ x 4 x 10 Area = 120 + 20 Area = 140m2 What Goes In The Box ? 2 Find the area of the shapes below : (1) 40cm2 (2) 10cm 6.3m 10.2 m 8cm 18m 32.13m2 (3) 12m 258m2 25m The Area Of A Circle. Consider the circle below divided into quarters: We are going to place the quarters as shown to make the shape below We can fit a rectangle around this shape: At the moment it is hard to see why this should tell us how to calculate the area of a circle. Now consider the same circle split into eight parts: The eight parts are arranged into the same pattern as last time: L B This time the shapes fit the rectangle more closely: L B This time the shapes fit the rectangle more closely: What length must the breadth B be close to ? B=r What length must the length L be close to ? Half of the circumference of the circle. If C = 2 r then L = r . We now have an approximate length and breadth of our rectangle. r . r What is the area of the rectangle ? A= r x r A= r 2 If the circle was split into more and more smaller segments and the segments arranged in the same pattern, then the parts would become the rectangle shown above. See “Autograph Extras”, “New”, “Area Of Circle” for further info’. r Conclusion. The area of a circle of radius r is given by the formula A = r 2. Find the area of the circles below: Example 1. Example 2 20 cm 2.7m A= r 2 A= r 2 r = 10 r = 1.35m A = 3.14 x 10 x 10 A = 3.14 x 1.35 x 1.35 A = 5.72m2 ( to 2 d.p) A = 314 cm2 Example 3 Example 4 7cm 7cm A1 A2 12cm 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 A = 12 x 7 + ½ x 3.14 x 3.5 x 3.5 2 A = 84 + 19.23 A = 76.93cm2 A = 103.2cm 2. (to 1 d.p) What Goes In The Box ? 4 Find the area of the shapes below : (1) (2) 6.3m 7cm 153.86cm2 31.16m2 ( 2 d.p) (3) 4.2cm 35.1cm 2 ( 1 d.p) 6.7cm

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posted: | 11/10/2011 |

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