Level 3 Areas of Simple Shapes This presentation will cover the formulae for the areas of various simple shapes. It is aimed at students studying at level 3. Where appropriate, follow up exercises are indicated for consolidation purposes. www.mathsrevision.com Wednesday, 05 April 2017 Created by Mr.Lafferty

Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special Areas www.mathsrevision.com Revision of Square, Rectangle and RAT. Any Type of Triangle Rhombus and kite Parallelogram Trapezium Wednesday, 05 April 2017 Created by Mr.Lafferty Composite shapes

Starter Questions Q1. Is the solution to the equation x = -3 Explain ao Q2. Are the missing angles ao = 45o and bo = 55o bo www.mathsrevision.com Q3. Explain why the mean is equal to 12 16, 9, 15,8 Q4. How many difference ways can you find Wednesday, 05 April 2017 Created by Mr.Lafferty

Revision of Area www.mathsrevision.com Learning Intention Success Criteria 1. To revise the basic areas including square, rectangles and RAT’s. To remember the area formula for the square, rectangle and RAT’s. www.mathsrevision.com Apply formulae correctly. (showing working) Answer containing appropriate units Wednesday, 05 April 2017 Created by Mr.Lafferty

Revision of Area Exercise 1 Teejay Page 101 The Square The Rectangle The RAT l b h l l b www.mathsrevision.com Exercise 1 Teejay Page 101 Wednesday, 05 April 2017 Created by Mr.Lafferty

Basic Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special Areas www.mathsrevision.com Revision of Square, Rectangle and RAT. Any Type of Triangle Rhombus and kite Parallelogram Trapezium Wednesday, 05 April 2017 Created by Mr.Lafferty

Starter Questions Q1. Calculate www.mathsrevision.com 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 Wednesday, 05 April 2017 Created by Mr.Lafferty

Any Triangle Area www.mathsrevision.com Learning Intention Success Criteria 1. To develop a formula for the area of ANY triangle. To remember the formula for the area of ANY triangle. www.mathsrevision.com Apply formula correctly. (showing working) Answer containing appropriate units Wednesday, 05 April 2017 Created by Mr.Lafferty

Sometimes called the altitude Any Triangle Area Demo h = vertical height Sometimes called the altitude h www.mathsrevision.com b Wednesday, 05 April 2017 Created by Mr.Lafferty

Any Triangle Area Example 1 : Find the area of the triangle. 6cm www.mathsrevision.com 8cm Wednesday, 05 April 2017 Created by Mr.Lafferty

Any Triangle Area Exercise 2 Teejay Page 104 Example 2 : Find the area of the triangle. Altitude h outside triangle this time. 10cm www.mathsrevision.com 4cm Exercise 2 Teejay Page 104 Wednesday, 05 April 2017 Created by Mr.Lafferty

Starter Questions 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 Wednesday, 05 April 2017 Created by Mr.Lafferty

Rhombus and Kite Area www.mathsrevision.com Learning Intention Success Criteria 1. To develop a single formula for the area of ANY rhombus and Kite. To remember the formula for the area of ANY rhombus and kite. www.mathsrevision.com Apply formulae correctly. (showing working) Answer containing appropriate units Wednesday, 05 April 2017 Created by Mr.Lafferty

Area of a Rhombus d www.mathsrevision.com D This part of the rhombus is half of the small rectangle. Area of a Rhombus d D www.mathsrevision.com Wednesday, 05 April 2017 Created by Mr.Lafferty

Area of a Kite Exactly the same process as the rhombus d www.mathsrevision.com Wednesday, 05 April 2017 Created by Mr.Lafferty

Rhombus and Kite Area 2cm 4cm www.mathsrevision.com 5cm 9cm Example 1 : Find the area of the shapes. 2cm 4cm 5cm 9cm www.mathsrevision.com Wednesday, 05 April 2017 Created by Mr.Lafferty

Rhombus and Kite Area Exercise 3 Teejay Page 107 Example 2 : Find the area of the V – shape kite. 4cm www.mathsrevision.com 7cm Exercise 3 Teejay Page 107 Wednesday, 05 April 2017 Created by Mr.Lafferty

Starter Questions Q1. Is the area of the rhombus equal to 10.5cm2 Explain your answer. 7cm Q2. Show that there are 2880 minutes in 2 days www.mathsrevision.com Q3. Expand 2p( y - 3p) – 2py Q4. Calculate Wednesday, 05 April 2017 Created by Mr.Lafferty

Parallelogram Area www.mathsrevision.com Learning Intention Success Criteria 1. To develop a formula for the area of a parallelogram. To remember the formula for the area of a parallelogram. www.mathsrevision.com Apply formula correctly. (showing working) Answer containing appropriate units Wednesday, 05 April 2017 Created by Mr.Lafferty

Parallelogram Area Important NOTE h = vertical height h b www.mathsrevision.com Wednesday, 05 April 2017 Created by Mr.Lafferty

Parallelogram Area Exercise 4 Teejay Page 110 Example 1 : Find the area of parallelogram. 3cm www.mathsrevision.com 9cm Exercise 4 Teejay Page 110 Wednesday, 05 April 2017 Created by Mr.Lafferty

Starter Questions 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 Wednesday, 05 April 2017 Created by Mr.Lafferty

Trapezium Area www.mathsrevision.com Learning Intention Success Criteria 1. To develop a formula for the area of a trapezium. To remember the formula for the area of a trapezium. www.mathsrevision.com Apply formula correctly. (showing working) Answer containing appropriate units Wednesday, 05 April 2017 Created by Mr.Lafferty

Trapezium Area Two triangles WXY and WYZ a cm X Y 1 h cm 2 www.mathsrevision.com W Z b cm Wednesday, 05 April 2017 Created by Mr.Lafferty

Trapezium Area Exercise 5 Teejay Page 112 Example 1 : Find the area of the trapezium. 5cm 4cm www.mathsrevision.com 6cm Exercise 5 Teejay Page 112 Wednesday, 05 April 2017 Created by Mr.Lafferty

Starter Questions Q1. Find the area of the trapezium 9 Q1. Find the area of the trapezium 8 7 Q2. Is the HCF for 4 and 12 equal to 2. Explain your answer. www.mathsrevision.com Q3. Find 6.5% of 60 Q4. Is 3(f – 4) - 4f = 7f -12 Explain your answer Wednesday, 05 April 2017 Created by Mr.Lafferty

Composite Areas www.mathsrevision.com Learning Intention Success Criteria 1. To show how we can apply basic area formulae to solve more complicated shapes. To understand the term composite. www.mathsrevision.com 2. To apply basic formulae to solve composite shapes. Answer containing appropriate units Wednesday, 05 April 2017 Created by Mr.Lafferty

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 3cm 6cm 4cm Wednesday, 05 April 2017 Created by Mr.Lafferty

Composite Areas Exercise 6 Teejay Page 114 Example 2 : Find the area of the shaded area. 8cm 11cm www.mathsrevision.com 4cm 10cm Exercise 6 Teejay Page 114 Wednesday, 05 April 2017 Created by Mr.Lafferty