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Area Of Sha p es.

2cm. 12m. A1. A2. 7cm. 10m. 5cm. A1. 3cm. 12cm. A2. 16m. 8cm. Area Of Sha p es. 1cm 2. 1cm. 1cm. 1cm 2. 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.

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Area Of Sha p es.

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  1. 2cm 12m A1 A2 7cm 10m 5cm A1 3cm 12cm A2 16m 8cm Area Of Shapes.

  2. 1cm2 1cm 1cm 1cm2 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. A square centimetre is a square measuring one centimetre in each direction. It is written as :

  3. B A C D Estimating The Area. Look at the four shapes below and use your judgement to order them from smallest to largest area:

  4. 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.

  5. Breadth Length C A = LB for short. Area Of A Rectangle. Look again at one of the shapes whose area we estimated: 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

  6. We can now calculate the area of each rectangle very quickly: (1) (2) (3) (4) A= L x B A = 12 x 3 =36cm2 A= L x B A = 6 x 6 =36cm2 A= L x B A= L x B A = 18 x 2 =36cm2 A = 9 x 4 =36cm2

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

  8. 2cm 5cm A1 A1 3cm A2 A2 8cm Example 3. Solution. Split the shape up into two rectangles: Calculate the area of A1 and A2. 2 3 5 6 Calculate the area of the shape above: Area = A1 + A2 Area = ( 2 x 5) + (6 x 3) Area = 10 + 18 Area = 28cm2

  9. (1) (2) 6cm 2.7m 8cm 4.2m 17cm (3) 5cm 12cm 8cm What Goes In The Box ? Find the area of the shapes below : 48cm2 11.34m2 141cm2

  10. 5cm Height 8 cm Base The Area Of A Triangle. Consider the right angled triangle below: What is the area of the triangle ? Area = ½ x 40 = 20cm2 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 = 8 x 5 = 40 cm2

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

  12. 6cm 3.2m 10cm 6.4m Calculate the areas of the triangles below: Example 1 Example 2 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 20.48 = 10.24m2

  13. 12m 10m A1 A1 16m A2 A2 Example 3. Calculate the area of the shape below: Solution. Divide the shape into parts: Area = A1 + A2 10 10 12 16-12 =4 Area = LB + 1/2 BH Area = 10 x 12 + ½ x 4 x 10 Area = 120 + 20 Area = 140m2

  14. (1) (2) 6.3m 10cm 10.2 m 8cm 18m (3) 12m 25m What Goes In The Box ? 2 Find the area of the shapes below : 40cm2 32.13m2 258m2

  15. The Area Of A Trapezium. A Trapezium is any closed shape which has two sides that are parallel and two sides that are not parallel.

  16. We are now going to find a formula for the area of the trapezium: b h a A1 A1 A2 A2 A3 A3 Area = A1 + ( A2 + A3 ) Area = b x h + ½ x (a - b) x h Area = bh + ½ h(a - b) Divide the shape into parts: Area = bh + ½ ah – ½ bh Area = ½ ah + ½ bh Work out the dimensions of the shapes: Area = ½ h ( a + b ) b h Often common sense is as good as the formula to work out the area of a trapezium. h a – b

  17. 11cm 13cm 16cm Example 1 Calculate the area of the trapezium below : Solution ( Using the formula). Area = ½ h ( a + b ) a = 16 b =11 h = 13 Area = ½ x 13 x ( 16 + 11 ) Area = ½ x 13 x 27 Area = 175.5cm2

  18. 11cm 13cm 16cm Solution ( Using composite shapes). Divide the shape into parts: Area = rectangle + triangle Area = LB + ½ BH Area = (11x 13) + ( ½ x 5 x 13 ) Area = 143 + 32.5 Area = 175.5cm2 11 Decide for yourself if you prefer the formula or composite shapes. 13 13 16 – 11 = 5

  19. 8m 14m 10m Example 2 Divide the shape into parts: Area = rectangle + triangle Area = LB + ½ B H A = ( 10 x 8 ) + ( ½ x 6 x 10 ) A = 80 + 30 A = 110 m 2 10 10 14 – 8 = 6 8

  20. 13cm (1) 10cm (2) 20cm 5.4m 4.9m 2.7m What Goes In The Box ? 3 Find the area of the shapes below : 165cm2 19.85m2 (to 2 d.p)

  21. 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.

  22. L B Now consider the same circle split into eight parts: The eight parts are arranged into the same pattern as last time: This time the shapes fit the rectangle more closely:

  23. B L 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.

  24.  r . r Conclusion. r The area of a circle of radius r is given by the formula A =  r 2. 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’.

  25. 2.7m 20 cm Find the area of the circles below: Example 2 Example 1. A =  r 2 A =  r 2 r = 1.35m r = 10 A = 3.14 x 1.35 x 1.35 A = 3.14 x 10 x 10 A = 5.72m2( to 2 d.p) A = 314 cm2

  26. A1 A2 7cm 7cm 12cm A =  r 2 2 A = 3.14 x 7 x 7 2 Example 4 Example 3 Split the shape into two areas. Find half the area of a circle: Area = A1 + A2 Area = LB + ½  r 2. L = 12 B = 7 r = 3.5 A = 12 x 7 + ½ x 3.14 x 3.5 x 3.5 A = 84 + 19.23 A = 76.93cm2 A = 103.2cm 2. (to 1 d.p)

  27. (1) (2) 6.3m 7cm (3) 4.2cm 6.7cm What Goes In The Box ? 4 Find the area of the shapes below : 153.86cm2 31.16m2 ( 2 d.p) 35.1cm 2 ( 1 d.p)

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