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Perimeter Of Shapes. 8cm 2cm 5cm 3cm A1 A2 16m 12m 10m 12cm 7cm

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What Is Perimeter ? Perimeter is the distance around a shape. Think of a fence. 9cm 4cm 4cm 9cm For example: Perimeter = = 26 cm

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Area Of Shapes. 8cm 2cm 5cm 3cm A1 A2 16m 12m 10m 12cm 7cm

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**What Is Area ? Area is the amount of space inside a shape: Area Area**

1cm Area is measured in square units. 1cm2 A square unit is a square measuring one unit in each direction. For example: It is written as :

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**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: A B C D

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**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.

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**Area Of A Rectangle. C Length Width**

The formula for the area of a rectangle is: A = LW for short. Area = Length x Width or

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**We can now calculate the area of each rectangle very quickly:**

(1) (2) A= L x W A = 12 x 3 =36cm2 (3) A= L x W A = 6 x 6 =36cm2 A= L x W A= L x W (4) A = 18 x 2 =36cm2 A = 9 x 4 =36cm2

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Example 1 Calculate the area of the rectangle below: (2) 3m 5m 7cm 4cm (1) Solution This area is in square metres: 1m A = LW Solution A = LW L = 7 W = 4 L = 3 W = 5 A = 7 x 4 A = 3 x 5 A = 28cm2 A = 15m2

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Example 3. Solution. 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 = Area = 28cm2

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**What Goes In The Box ? Find the area of the shapes below : (1) 8cm 6cm**

(2) 48cm2 (3) 17cm 8cm 12cm 5cm 11.34m2 141cm2

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**The Area Of A Triangle. Consider the right angled triangle below: 5cm**

Base Height What shape is the triangle half of ? The formula for the area of a triangle is: Rectangle Area = ½ x Base x Height What is the area of the rectangle? A = ½ BH Area = BH

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**Does the formula apply to all triangles ?**

Base (B) Height (H) Can we make this triangle into a rectangle ? Yes The triangle is half the area of this rectangle: The areas marked A1 are equal. B H A1 A2 The areas marked A2 are equal. For all triangles: Area = ½ BH

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**Calculate the areas of the triangles below:**

Example 1 Example 2 10cm 6cm 6.4m 3.2m Solution. Solution. Area = ½ x base x height Area = ½ x base x height height = 6cm base = 10 cm height = 3.2m base = 6.4m Area = ½ x 10 x 6 Area = ½ x 6.4 x 3.2 Area = ½ x 60 = 30cm2 Area = ½ x = 10.24m2

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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 = LW + 1/2 BH Area = 10 x ½ x 4 x 10 Area = Area = 140m2

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**What Goes In The Box ? Find the area of the shapes below : (1) 8cm**

(2) 10.2 m 6.3m 32.13m2 (3) 25m 18m 12m 258m2

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**The Area Of A Parallelogram.**

A Parallelogram is any closed shape which has two sets of parallel sides.

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**We are now going to find a formula for the area of a parallelogram:**

Divide the shape into parts: h b Area = b x h Height and Base have to be perpendicular

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Example 1 Calculate the area of the parallelogram below : Solution ( Using the formula). 16cm 13cm Area = b x h b = 16 h =13 Area = 16 x 13 Area = 208 cm2

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