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Simple Areas

Simple Areas. Definition : Area is “ how much space a shape takes up”. A few types of special Areas. www.mathsrevision.com. Counting Squares. Rectangle. RAT. Any Type of Triangle. Composite Area. Parallelogram. Rhombus and kite. Trapezium. Starter Questions. National 4 EF 1.2b.

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Simple Areas

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

  2. Starter Questions National 4 EF 1.2b Q1. Solve the equation below ao Q2. Find the missing angles bo Q3. Find the average of the numbers below www.mathsrevision.com 2,5,6,7 Q4. Which is the better deal or Created by Mr. Lafferty Maths Dept.

  3. National 4 EF 1.2b Area Counting Squares Learning Intention Success Criteria • To understand the term area. • 1. To explain area in terms of counting squares. • Find the area by counting squares. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  4. 1cm 1cm National 4 EF 1.2b Area Counting Squares The area of a shape is simply defined by : “the amount of space a shape takes up.” Think of a square measuring 1 cm by 1cm we say it is : www.mathsrevision.com 1cm2 ( 1 square centimetre ) Created by Mr. Lafferty Maths Dept.

  5. Area Counting Squares National 4 EF 1.2b Now try Exercise 1 Ch14 (page 163) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  6. National 4 EF 1.2b Starter Questions Q1. What is the time difference 09:28 and 11:55 Q2. www.mathsrevision.com Q3. Convert 23metres to (a) cm (b) mm Q4. The answer to the question is 180. What is the question. Created by Mr. Lafferty Maths Dept.

  7. National 4 EF 1.2b Area of a Rectangle Learning Intention Success Criteria • To be able to state area formula for a rectangle. • 1. To come up with a formula • for the area of a • rectangle. • Apply formula correctly. • (showing working) www.mathsrevision.com • Use the formula to solve problems. • Answer containing • appropriate units Created by Mr. Lafferty Maths Dept.

  8. 1 cm Area = length x breadth L B A A = L x B = X = X = X National 4 EF 1.2b Area of a Rectangle B B L L L = length www.mathsrevision.com L B B = Breadth 3 1 3 4 3 12 Must learn formula ! 3 2 6 Created by Mr. Lafferty Maths Dept.

  9. National 4 EF 1.2b Example Area of a Rectangle Find the area of the rectangle B = 2cm L = 9cm Area = Length x Breadth A = L x B www.mathsrevision.com A = 9 x 2 A = 18 cm2 Created by Mr. Lafferty Maths Dept.

  10. National 4 EF 1.2b Example Area of a Rectangle Find the length B of the rectangle opposite A = 36cm2 B cm L = 12cm Area = Length x Breadth Balancing Method A = L x B www.mathsrevision.com 36 = 12 x B Remember units Created by Mr. Lafferty Maths Dept.

  11. Area of a Rectangle National 4 EF 1.2b Now try Exercise 2 Ch14 (page 167) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  12. Starter Questions National 4 EF 1.2b Q1. Calculate 110o Q2. Are the missing angles 70o,40o,40o Explain www.mathsrevision.com Q3. Is the HCF of 10 and 36 180 Explain. Q4. Explain 2 ways of calculating Created by Mr.Lafferty

  13. 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

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

  15. 8cm Any Triangle Area Example 1 : Find the area of the triangle. 6cm www.mathsrevision.com Created by Mr.Lafferty

  16. 4cm Any Triangle Area National 4 EF 1.2b Example 2 : Find the area of the triangle. Altitude h outside triangle this time. 10cm www.mathsrevision.com Created by Mr.Lafferty

  17. Area of ANY Triangle National 4 EF 1.2b Now try Exercise 4 Ch14 (page 174) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  18. National 4 EF 1.2b Starter Questions Q1. Why is Q2. What is the time difference 07:54 and 13:36 Q3. www.mathsrevision.com Q4. Convert 45.1 metres to (a) cm (b) mm Q5. The answer to the question is 90. What is the question. Created by Mr. Lafferty Maths Dept.

  19. National 4 EF 1.2b Made up of Simple shapes Area of a Composite Learning Intention Success Criteria • To be able to use knowledge gained so far to find the area of more complicated shapes.. • 1. To use knowledge to find area of more complicate shapes. www.mathsrevision.com • Show appropriate working. Created by Mr. Lafferty Maths Dept.

  20. 9cm 6cm 8cm 5cm Area of a Composite National 4 EF 1.2b Calculate the area of this shape Total Area = 72 + 30 = 102cm2 A = l x b A = 9 x 8 www.mathsrevision.com A = l x b A = 72cm2 A = 6 x 5 A = 30cm2 Created by Mr. Lafferty Maths Dept.

  21. 8cm 10cm 6cm 12cm Area of a Composite National 4 EF 1.2b Calculate the area of this shape www.mathsrevision.com

  22. 8cm 10cm 6cm 4cm Area of a Composite National 4 EF 1.2b Calculate the area of this shape Total Area = 80 + 24 = 104cm2 A = l x b www.mathsrevision.com A = 8 x 10 A = l x b A = 80cm2 A = 4 x 6 A =24cm2

  23. 5cm 6cm Area of a Composite National 4 EF 1.2b Calculate the area of this shape 16cm Rectangle 1 A = l x b A = 16 x 5 5cm A = 80cm2 www.mathsrevision.com Rectangle 2 A = l x b Total Area A = 6 x 5 = 80 + 30 =110cm2 A = 30cm2 Created by Mr. Lafferty Maths Dept.

  24. Area of a Composite National 4 EF 1.2b Now try Exercise 5 Ch14 (page 176) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  25. Starter Questions National 4 EF 1.2b Q1. 40% of £90 Q2. Show that there are 2880 minutes in 2 days www.mathsrevision.com Q3. Expand 2( y - 3p) – 2y Q4. Calculate Created by Mr.Lafferty

  26. 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

  27. h b Parallelogram Area National 4 EF 1.2b Important NOTE h = vertical height www.mathsrevision.com Created by Mr.Lafferty

  28. Parallelogram Area National 4 EF 1.2b Example 1 : Find the area of parallelogram. 3cm www.mathsrevision.com 9cm Created by Mr.Lafferty

  29. Area of a Parallelogram National 4 EF 1.2b Now try Extension Booklet 2E(a) (page 71) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  30. Starter Questions National 4 EF 1.2b Q1. Find the area of the triangle. 3cm Q2. Expand out 2w( w - 5) – 3w 4cm www.mathsrevision.com Q3. Calculate Q4. Find the LCM of the two numbers 4 and 6 Created by Mr.Lafferty

  31. 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

  32. This part of the rhombus is half of the small rectangle. d D Area of a Rhombus National 4 EF 1.2b www.mathsrevision.com Created by Mr.Lafferty

  33. d D Area of a Kite Exactly the same process as the rhombus National 4 EF 1.2b www.mathsrevision.com Created by Mr.Lafferty

  34. Rhombus and Kite Area National 4 EF 1.2b Example 1 : Find the area of the shapes. 2cm 4cm 5cm 9cm www.mathsrevision.com Created by Mr.Lafferty

  35. Area of a Kite & Rhombus National 4 EF 1.2b Now try Extension Booklet 2E(b) (page 75) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  36. Starter Questions National 4 EF 1.2b Q1. Find the area of the parallelogram 8 7 Q2. Is the HCF 6 and 24 24 Explain your answer. www.mathsrevision.com Q3. Show that 11.5 % of 150 is 17.25 Q4. Simplify 3(h -2) + h(2 - 4h) = -4h2 + 6h - 6 Created by Mr.Lafferty

  37. 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

  38. Trapezium Area National 4 EF 1.2b Two triangles WXY and WYZ a cm X Y 1 h cm 2 www.mathsrevision.com Z W b cm Created by Mr.Lafferty

  39. Trapezium Area National 4 EF 1.2b Example 1 : Find the area of the trapezium. 5cm 4cm www.mathsrevision.com 6cm Created by Mr.Lafferty

  40. Area of a Trapezium National 4 EF 1.2b Now try Extension Booklet 6E (page 78) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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