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## Area of Any Triangle

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**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**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**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**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**h = vertical height**b Any Triangle Area Sometimes called the altitude h www.mathsrevision.com Created by Mr.Lafferty**8cm**Any Triangle Area Example 1 : Find the area of the triangle. 6cm www.mathsrevision.com Created by Mr.Lafferty**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**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**Area & Volume**Now try Ex 2.1 & 2.2 MIA Ch1 (page 6) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com**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**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**h**b Parallelogram Area Important NOTE h = vertical height www.mathsrevision.com Created by Mr.Lafferty**Parallelogram Area**Example 1 : Find the area of parallelogram. 3cm www.mathsrevision.com 9cm Created by Mr.Lafferty**Area & Volume**Now try Ex 3.1 MIA Ch1 (page 6) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com**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**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**This part of**the rhombus is half of the small rectangle. d D Area of a Rhombus www.mathsrevision.com Created by Mr.Lafferty**d**D Area of a Kite Exactly the same process as the rhombus www.mathsrevision.com Created by Mr.Lafferty**Rhombus and Kite Area**Example 1 : Find the area of the shapes. 2cm 4cm 5cm 9cm www.mathsrevision.com Created by Mr.Lafferty**Rhombus and Kite Area**Example 2 : Find the area of the V – shape kite. 4cm www.mathsrevision.com 7cm Created by Mr.Lafferty**Area & Volume**Now try Ex 4.1 MIA Ch1 (page 8) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com**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**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**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**Trapezium Area**Example 1 : Find the area of the trapezium. 5cm 4cm www.mathsrevision.com 6cm Created by Mr.Lafferty**Area & Volume**Now try Ex 5.1 MIA Ch1 (page 9) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com**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**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**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**Composite Areas**Example 2 : Find the area of the shaded area. 8cm 11cm www.mathsrevision.com 4cm 10cm Created by Mr.Lafferty**Area & Volume**Now try Ex 6.1 MIA Ch1 (page 11) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com**Summary Areas**Rhombus and kite Any Type of Triangle www.mathsrevision.com Trapezium Parallelogram**Area & Volume**Now try Ex 6.2 MIA Ch1 (page 12) www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com**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**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.**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**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**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**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.**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.**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.**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.**Volume of Solids**Now try MIA Ex 7.1 & 7.2 Ch1 (page 14) www.mathsrevision.com**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**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**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**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**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**Surface Area**of a Cylinder Now try MIA Ex 8.1 Ch1 (page 16) www.mathsrevision.com**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