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Area of Any Triangle

Volume of Solids. Area of Any Triangle. Area of Parallelogram. Area of Kite & Rhombus. Area of Trapezium. Composite Area. www.mathsrevision.com. Volume & Surface Area. Surface Area of a Cylinder. Exam Type Questions. Volume of a Cylinder. Composite Volume. Starter Questions.

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Area of Any Triangle

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  1. Volume of Solids Area of Any Triangle Area of Parallelogram Area of Kite & Rhombus Area of Trapezium Composite Area www.mathsrevision.com Volume & Surface Area Surface Area of a Cylinder Exam Type Questions Volume of a Cylinder Composite Volume

  2. Starter Questions Q1. True or false Q2. Write down the probability of picking out a number greater than 20 in the national lottery. www.mathsrevision.com Q3. If a = -3 and b = -4 does a2 – 3b2 = 57 Q4. Calculate Created by Mr.Lafferty

  3. Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special Areas www.mathsrevision.com Any Type of Triangle Parallelogram Rhombus and kite Trapezium Created by Mr.Lafferty

  4. Any Triangle Area Learning Intention Success Criteria • To know the formula for the area of ANY triangle. • 1. To develop a formula for the area of ANY triangle. www.mathsrevision.com • Apply formula correctly. • (showing working) • Use the formula to solve problems. • Answer containing • appropriate units Created by Mr.Lafferty

  5. h = vertical height b Any Triangle Area Sometimes called the altitude h www.mathsrevision.com Created by Mr.Lafferty

  6. 8cm Any Triangle Area Example 1 : Find the area of the triangle. 6cm www.mathsrevision.com Created by Mr.Lafferty

  7. 4cm Any Triangle Area Example 2 : Find the area of the triangle. Altitude h outside triangle this time. 10cm www.mathsrevision.com Created by Mr.Lafferty

  8. Hint : Use Pythagoras Theorem first ! 8cm Any Triangle Area Example 3 : Find the area of the isosceles triangle. 5cm www.mathsrevision.com 4cm Created by Mr.Lafferty

  9. Area & Volume Now try Ex 2.1 & 2.2 MIA Ch1 (page 6) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  10. Starter Questions 10cm Q1. Find the area of the triangle. 3cm Q2. Expand out ( w - 5) (2w2 + 2w – 5) 4cm www.mathsrevision.com Q3. True or false Q4. Rearrange into the form y = y – 3x + 7 = 0 Created by Mr.Lafferty

  11. Parallelogram Area Learning Intention Success Criteria • To know the formula for the area of a parallelogram. • 1. To develop a formula for the area of a parallelogram. www.mathsrevision.com • Apply formula correctly. • (showing working) • Use the formula to solve problems. • Answer containing • appropriate units Created by Mr.Lafferty

  12. h b Parallelogram Area Important NOTE h = vertical height www.mathsrevision.com Created by Mr.Lafferty

  13. Parallelogram Area Example 1 : Find the area of parallelogram. 3cm www.mathsrevision.com 9cm Created by Mr.Lafferty

  14. Area & Volume Now try Ex 3.1 MIA Ch1 (page 6) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  15. Starter Questions Q1. True or false 2x2 – 72 = 2(x – 6)(x + 6) Q2. Does 2.5 + 1.25 x 20 = 27.55 Explain your answer www.mathsrevision.com Q3. Expand ( y - 3) (2y2 + 3y + 2) Q4. Calculate Created by Mr.Lafferty

  16. Rhombus and Kite Area Learning Intention Success Criteria • To know the formula for the area of ANY rhombus and kite. • 1. To develop a single formula for the area of ANY rhombus and Kite. www.mathsrevision.com • Apply formulae correctly. • (showing working) • Use the formula to solve problems. • Answer containing • appropriate units Created by Mr.Lafferty

  17. This part of the rhombus is half of the small rectangle. d D Area of a Rhombus www.mathsrevision.com Created by Mr.Lafferty

  18. d D Area of a Kite Exactly the same process as the rhombus www.mathsrevision.com Created by Mr.Lafferty

  19. Rhombus and Kite Area Example 1 : Find the area of the shapes. 2cm 4cm 5cm 9cm www.mathsrevision.com Created by Mr.Lafferty

  20. Rhombus and Kite Area Example 2 : Find the area of the V – shape kite. 4cm www.mathsrevision.com 7cm Created by Mr.Lafferty

  21. Area & Volume Now try Ex 4.1 MIA Ch1 (page 8) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  22. Starter Questions Q1. Find the area of the parallelogram 7 7 Q2. Solve the equation (ie find the root) to 1 dp x2 + 4x – 3 = 0 www.mathsrevision.com Q3. A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4. The speed of light is 300000000 metres per sec. True or false in scientific notation 3 x 108. Created by Mr.Lafferty

  23. Trapezium Area Learning Intention Success Criteria • To know the formula for the area of a trapezium. • 1. To develop a formula for the area of a trapezium. www.mathsrevision.com • Apply formula correctly. • (showing working) • Use the formula to solve problems. • Answer containing • appropriate units Created by Mr.Lafferty

  24. Trapezium Area Two triangles WXY and WYZ a cm X Y 1 h cm 2 www.mathsrevision.com Z W b cm Created by Mr.Lafferty

  25. Trapezium Area Example 1 : Find the area of the trapezium. 5cm 4cm www.mathsrevision.com 6cm Created by Mr.Lafferty

  26. Area & Volume Now try Ex 5.1 MIA Ch1 (page 9) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  27. Starter Questions 9 8 Q1. Find the area of the trapezium 7 Q2. Explain why the perimeter of the shape is 25.24cm. 30o www.mathsrevision.com r = 10cm Q3. y varies directly as the square of x. When y = 25 , x = 4 Find the value of y when x = 10 Created by Mr.Lafferty

  28. Composite Areas Learning Intention Success Criteria • To know the term composite. • 1. To show how we can apply basic area formulae to solve more complicated shapes. www.mathsrevision.com 2. To apply basic formulae to solve composite shapes. • Answer containing • appropriate units Created by Mr.Lafferty

  29. Composite Areas We can use our knowledge of the basic areas to work out more complicated shapes. Example 1 : Find the area of the arrow. www.mathsrevision.com 5cm 6cm 3cm 4cm Created by Mr.Lafferty

  30. Composite Areas Example 2 : Find the area of the shaded area. 8cm 11cm www.mathsrevision.com 4cm 10cm Created by Mr.Lafferty

  31. Area & Volume Now try Ex 6.1 MIA Ch1 (page 11) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  32. Summary Areas Rhombus and kite Any Type of Triangle www.mathsrevision.com Trapezium Parallelogram

  33. Area & Volume Now try Ex 6.2 MIA Ch1 (page 12) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

  34. Starter Questions 9 8 Q1. Find the area of the trapezium 7 Q2. Calculate the perimeter of the shape. 60o www.mathsrevision.com r = 3cm Q3. w varies inversely as the square of b. When w = 10 , b = 2 Find the value of w when b = 10 Created by Mr.Lafferty

  35. Volume of Solids Prisms Learning Intention Success Criteria • To know the volume formula for any prism. • To understand the • prism formula for calculating volume. • Work out volumes for • various prisms. www.mathsrevision.com • Answer to contain • appropriate units and working.

  36. Volume of Solids Definition : A prism is a solid shape with uniform cross-section www.mathsrevision.com Hexagonal Prism Cylinder (circular Prism) Triangular Prism Pentagonal Prism Volume = Area of Cross section x length

  37. Volume of Solids Definition : A prism is a solid shape with uniform cross-section Q. Find the volume the triangular prism. www.mathsrevision.com Triangular Prism Volume = Area x length = 20 x 10 = 200 cm3 10cm 20cm2

  38. Volume of Solids Definition : A prism is a solid shape with uniform cross-section Q. Find the volume the hexagonal prism. 43.2cm2 www.mathsrevision.com Volume = Area x length 20cm Hexagonal Prism = 43.2 x 20 = 864 cm3

  39. Front Back Bottom 4cm 4cm FT BT 10cm 4cm 4cm 10cm Net and Surface Area Triangular Prism www.mathsrevision.com 5 faces 3 congruent rectangles 2 congruent triangles This is a NET for the triangular prism. Created by Mr. Lafferty Maths Dept.

  40. Triangle Area = 4cm Example Find the surface area of the right angle prism Working = 2 x3 =6cm2 Rectangle 1 Area = l x b = 3 x10 =30cm2 5cm Rectangle 2 Area = l x b 3cm 10cm = 4 x 10 =40cm2 www.mathsrevision.com Rectangle 3 Area = l x b = 5 x 10 =50cm2 2 triangles the same Total Area = 6+6+30+40+50 = 132cm2 1 rectangle 3cm by 10cm 1 rectangle 4cm by 10cm 1 rectangle 5cm by 10cm Compiled by Mr. Lafferty Maths Dept.

  41. Front 3cm Back RS LS 4cm 3cm Top 4cm Bottom 5cm Net and Surface Area The Cuboid 4cm 3cm www.mathsrevision.com 5cm 6 faces Top and bottom congruent Front and back congruent This is a NET for the cuboid Left and right congruent Compiled by Mr. Lafferty Maths Dept.

  42. Example Find the surface area of the cuboid Working Front Area = l x b = 5 x 4 =20cm2 Top Area = l x b = 5 x 3 =15cm2 4cm Side Area = l x b = 3 x 4 =12cm2 3cm www.mathsrevision.com Total Area = 20+20+15+15+12+12 = 94cm2 5cm Front and back are the same Top and bottom are the same Right and left are the same Compiled by Mr. Lafferty Maths Dept.

  43. Volume of Solids Now try MIA Ex 7.1 & 7.2 Ch1 (page 14) www.mathsrevision.com

  44. Starter Questions Q1. Expand out (x – 2) ( x2 - 3x + 4) Q2. Factorise x2 – 2x + 1 www.mathsrevision.com Q3. True or false Q4. By rearranging in y = , find the gradient and where the straight line crosses the x-axis y + 4x - 3 = 0 Created by Mr.Lafferty

  45. Surface Area of a Cylinder Learning Intention Success Criteria • To know split up a cylinder. • To explain how to calculate the surface area of a cylinder by using basic area. 2. Calculate the surface area of a cylinder. www.mathsrevision.com

  46. Surface Area of a Cylinder The surface area of a cylinder is made up of 2 basic shapes can you name them. Cylinder (circular Prism) Curved Area =2πrh 2πr Top Area =πr2 h Roll out curve side  Bottom Area =πr2 www.mathsrevision.com Total Surface Area = 2πr2 + 2πrh

  47. Surface Area of a Cylinder Example : Find the surface area of the cylinder below: 3cm Surface Area = 2πr2 + 2πrh 10cm = 2π(3)2 +2πx 3 x 10 www.mathsrevision.com = 18π + 60π Cylinder (circular Prism) = 78π cm

  48. Surface Area of a Cylinder Diameter = 2r Example : A net of a cylinder is given below. Find the diameter of the tin and the total surface area. 2πr = 25 25 9cm 25cm 2r = www.mathsrevision.com π Surface Area = 2πr2 + 2πrh = 2π(25/2π)2 + 2π(25/2π)x9 = 625/2π + 25x9 = 324.5 cm

  49. Surface Area of a Cylinder Now try MIA Ex 8.1 Ch1 (page 16) www.mathsrevision.com

  50. Starter Questions Q1. Find the area of the triangle. 10cm Q2. Factorise 9x2 - 64 6cm www.mathsrevision.com Q3. Calculate Q4. Find the gradient and where the straight line crosses the x-axis y – 2x + 5 = 0 Created by Mr.Lafferty

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