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## Perimeter, Area and Volume

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**Perimeter, Area and Volume**Grades F to A**Rectangles and Triangles**Hyperlinks! Counting Squares Parallelograms and Trapeziums Area – working backwards Circles Compound Shapes Volume of cuboids Volume of prisms Surface area Sectors of circles Volume and surface area of complex shapes**Area and perimeter by counting and measuring**How do I find the area and perimeter of a shape? Grade F**What are perimeter and area?**Perimeter is the length around the outside of a shape. Area is the space inside a shape.**Example**The rectangle has a perimeter of: 5 + 3 + 5 + 3 = 16cm The rectangle has a area of: 5 + 5 + 5 = 15cm² Take note of the units! 5 × 3 = 15cm²**Find the perimeter and area of this rectangle:**Perimeter = Area = 20cm 24cm²**Rectangles and Triangles**Can I calculate the perimeter and area of a rectangle and triangle? Grade E**Two examples:**Example 1 Example 2 Find the area of this triangle: Area = 5 × 12 ÷ 2 Area = 60cm² ÷ 2 Area = 30cm² Find the area and perimeter of this rectangle: Area = 8 × 6 Area = 48cm² Perimeter = 8 + 6 + 8 + 6 Perimeter = 28cm 13cm 6cm 5cm 8cm 12cm**Have a go at some:**Question 1 Question 2 Find the perimeter and area of this rectangle: Find the area of this triangle: 11cm 8cm 7cm 10cm Answer: Area = 88cm² Perimeter = 38cm Answer: 35cm²**Parallelograms and Trapeziums**Can I calculate the area of a parallelogram and trapezium? Grade D**Two examples**Example 1 Example 2 Find the area of this parallelogram: Area = 7 × 5 Area = 35cm² 4cm 5cm 6cm 5cm 7cm 8cm**Have a go at a couple of questions:**Question 1 Question 2 Find the area of this trapezium: Find the area of this parallelogram: 12cm 9cm 8cm 10cm 7cm 11cm Answer: 96cm² Answer: 70cm²**Circles**Can I find the circumference and area of a circle? Grade C**Names to do with circles you must remember:**Circumference Radius Diameter Chord Tangent**A couple of examples**Example 1 Example 2 Find the circumference and area of a circle with a radius of 8cm to 1 dp. Circumference = π × 16 Circumference = 50.3cm Area = π× 8² Area = 201.1cm² Find the circumference and area of a circle with a diameter of 10cm to 1 dp. Circumference = π × 10 Circumference = 31.4cm Area = π× 5² Area = 78.5cm²**Some for you to try:**Question 1 Question 2 Find the circumference and area of a circular pond with a diameter of 3m to 1 dp. Find the circumference and area of this circle to 1 dp. 14cm Circumference = 88.0cm Area = 615.8cm² Circumference = 9.4m Area = 7.1m²**Area – Working Backwards**Now you can find the area of shapes, can you find a length having been given the area?**Find the missing lengths:**None of these are drawn to scale ?cm 7cm 6cm Area = 48cm² Area = 21cm² 8cm ?cm 6cm 5cm 8cm ?cm Area = 113.1cm² Area = 32cm² Area = 28cm² 9cm Height = ? 4cm Height = 4cm 12cm Diameter = ?**Compound Shapes**Can I calculate the perimeter and area of a compound shape? Grade C**What is a compound shape?**A compound shape is a shape that is made up of lots of different shapes. The key is to split the complex shape up into simpler shapes, find the areas of the simple shapes then add your areas together.**An example**Find the area of this shape: Split it up! Area = 40 + 32 = 72cm² 12cm Area = 8×5 = 40cm² Area = 8×4 = 32cm² 8cm 8cm 3cm**Another example**Find the area of this shape: Split it up! Area = 54 + 13.5 = 67.5cm² 3m Area = 9×6 = 54m² 6m 9m**A couple of questions:**Question 1 Question 2 Find the area of this shape: Find the area of this shape: 12cm 3cm 5cm 8m 6cm 10m Answer: 66cm² Answer: 119.3m²**Volume of Cuboids**Can I calculate the volume of a cuboid? Grade C**An example:**Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³ 3cm 4cm 5cm Take note of the units!**Another example, working backwards:**Find the height of this cuboid: 280cm³ = 10 × 7 × h h = 280 ÷ (10 × 7) h = 4cm Volume = 280cm³ 7cm 10cm**Two questions to have a go at:**Question 1 Question 2 The tank below contains exactly 100 litres of water. How far up the tank does the water go? (Hint: 1 litre = 1000cm³) Find the volume of this cuboid: 8cm 6cm 0.5m 5cm 0.5m 1m Answer: 240cm³ Answer: 0.2m or 20cm**Prisms**Can I calculate the volume of a prism? Grade C**What is a prism?**A prism is a 3D shape that has the same cross-section all the way through. For example: Triangular Prism Hexagonal Prism Cylinder**Calculating the volume of a prism:**Find the area of the cross-section then multiply by the length. Volume = Area of cross-section × length