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Area of a parallelogram

Area of a parallelogram. Area of a parallelogram = base × perpendicular height. perpendicular height. base. Area of a parallelogram = bh. The area of any parallelogram can be found using the formula:. Or using letter symbols,. Area of a trapezium.

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Area of a parallelogram

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  1. Area of a parallelogram Area of a parallelogram = base × perpendicular height perpendicular height base Area of a parallelogram = bh The area of any parallelogram can be found using the formula: Or using letter symbols,

  2. Area of a trapezium Area of a trapezium = (sum of parallel sides) × height a perpendicular height b 1 1 2 2 Area of a trapezium = (a + b)h The area of any trapezium can be found using the formula: Or using letter symbols,

  3. Area of a trapezium = × 20 × 9 = (6 + 14) × 9 1 1 1 2 2 2 Area of a trapezium = (a + b)h What is the area of this trapezium? 6 m 9 m 14 m = 90 m2

  4. Area of a trapezium = × 11 × 12 = (8 + 3) × 12 1 1 1 2 2 2 Area of a trapezium = (a + b)h What is the area of this trapezium? 8 m 3 m 12 m = 66 m2

  5. Area problems This diagram shows a yellow square inside a blue square. What is the area of the yellow square? 3 cm 7 cm We can work this out by subtracting the area of the four blue triangles from the area of the whole blue square. 10 cm If the height of each blue triangle is 7 cm, then the base is 3 cm. Area of each blue triangle = ½ × 7 × 3 = ½ × 21 = 10.5 cm2

  6. Area problems 7 cm 10 cm This diagram shows a yellow square inside a blue square. What is the area of the yellow square? 3 cm We can work this out by subtracting the area of the four blue triangles from the area of the whole blue square. There are four blue triangles so, Area of four triangles = 4 × 10.5 = 42 cm2 Area of blue square = 10 × 10 = 100 cm2 Area of yellow square = 100 – 42 = 58 cm2

  7. Area formulae of 2-D shapes h b h b a h 1 1 2 2 Area of a triangle = bh Area of a trapezium = (a + b)h b You should know the following formulae: Area of a parallelogram = bh

  8. S8 Perimeter, area and volume Contents S8.1 Perimeter S8.2 Area S8.3 Surface area S8.5 Circumference of a circle S8.4 Volume S8.6 Area of a circle

  9. The value of π π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)! For any circle the circumference is always just over three times bigger than the radius. The exact number is called π (pi). We use the symbol π because the number cannot be written exactly.

  10. Approximations for the value of π Better approximations are 3.14 or . 22 7 When we are doing calculations involving the value π we have to use an approximation for the value. For a rough approximation we can use 3. We can also use the π button on a calculator. Most questions will tell you what approximations to use. When a calculation has lots of steps we write π as a symbol throughout and evaluate it at the end, if necessary.

  11. The circumference of a circle circumference π = diameter C π = d For any circle, or, We can rearrange this to make an formula to find the circumference of a circle given its diameter. C = πd

  12. The circumference of a circle Use π = 3.14 to find the circumference of this circle. C = πd 8 cm = 3.14 × 8 = 25.12 cm

  13. Finding the circumference given the radius The diameter of a circle is two times its radius, or d = 2r We can substitute this into the formula C = πd to give us a formula to find the circumference of a circle given its radius. C = 2πr

  14. The circumference of a circle 9 m 4 cm 58 cm 23 mm Use π = 3.14 to find the circumference of the following circles: C = πd C = 2πr = 3.14 × 4 = 2 × 3.14 × 9 = 12.56 cm = 56.52 m C = πd C = 2πr = 3.14 × 23 = 2 × 3.14 × 58 = 72.22 mm = 364.24 cm

  15. Finding the radius given the circumference C = 2π 12 2 × 3.14 Use π = 3.14 to find the radius of this circle. C = 2πr 12 cm How can we rearrange this to make r the subject of the formula? r = ? = 1.91 cm (to 2 d.p.)

  16. Find the perimeter of this shape Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 13 cm 6 cm Perimeter = 3.14 × 13 + 6 + 6 = 52.82 cm

  17. Circumference problem The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km? Using C = πd and π = 3.14, The circumference of the wheel = 3.14 × 50 = 157 cm 1 km = 100 000 cm 50 cm The number of complete rotations = 100 000 ÷ 157 = 636

  18. S8 Perimeter, area and volume Contents S8.1 Perimeter S8.2 Area S8.3 Surface area S8.6 Area of a circle S8.4 Volume S8.5 Circumference of a circle

  19. Area of a circle

  20. Formula for the area of a circle We can find the area of a circle using the formula Area of a circle = π×r×r or radius Area of a circle = πr2

  21. The area of a circle Use π = 3.14 to find the area of this circle. 4 cm A = πr2 = 3.14 × 4 × 4 = 50.24 cm2

  22. Finding the area given the diameter d r = 2 πd2 A = 4 The radius of a circle is half of its radius, or We can substitute this into the formula A = πr2 to give us a formula to find the area of a circle given its diameter.

  23. The area of a circle 2 cm 10 m 78 cm 23 mm Use π = 3.14 to find the area of the following circles: A = πr2 A = πr2 = 3.14 × 22 = 3.14 × 52 = 12.56 cm2 = 78.5 m2 A = πr2 A = πr2 = 3.14 × 232 = 3.14 × 392 = 1661.06 mm2 = 4775.94 cm2

  24. Find the area of this shape Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm. Area of circle = 3.14 × 6.52 13 cm 6 cm = 132.665 cm2 Area of rectangle = 6 × 13 = 78 cm2 Total area = 132.665 + 78 = 210.665 cm2

  25. Area of a sector Area of the sector = × π × 52 72° = × π × 52 360° 1 5 What is the area of this sector? 72° 5 cm = π × 5 = 15.7 cm2 (to 1 d.p.) We can use this method to find the area of any sector.

  26. Area problem Area of sector = × π × 122 1 4 Find the shaded area to 2 decimal places. Area of the square = 12 × 12 = 144 cm2 = 36π Shaded area = 144 – 36π 12 cm = 30.9 cm2 (to 1 d.p.)

  27. Area of a sector Area of the sector = × π × 10 72° = × π × 10 360° 1 5 What is the area of this sector? 72° 5 cm = π × 2 = 6.28 cm2 (to 1 d.p.) We can use this method to find the length of any arc.

  28. Formulae for circles r r You should know the following formulae: Circumference = πd and π = 3.14 Area of circle = πr2 Area of sector = a πr2 360 r a r a Length of the arc = a πd 360

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