 G K Powers 2013 Cambridge University Press 8. Applications of perimeter, area and volume Study guide 1

 G K Powers 2013 Cambridge University Press Pythagoras’ theorem Pythagoras’ theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. HSC Hint – Hypotenuse is always the longest side. 2

 G K Powers 2013 Cambridge University Press Perimeter Perimeter is the total length of the outside edges of a shape. It is the distance of the boundary. Triangle Quadrilateral Square Rectangle Circle HSC Hint – Check the length of all the sides in a composite shape have been included in the perimeter. 3

 G K Powers 2013 Cambridge University Press Area Area is the amount of surface enclosed by the boundaries of a shape. Triangle Square Rectangle Parallelogram Trapezium Rhombus Circle HSC Hint – Start area questions by writing the formula or the substitution into the formula. 4

 G K Powers 2013 Cambridge University Press Area of composite shapes  Composite shapes are made up of more than one simple shape.  Area of composite shapes can be found by adding or subtracting the areas of the simple shapes. Divide this shape into a square and a semicircle. Add the two areas. HSC Hint – On the diagram, divide the composite area into plane shapes. 5

 G K Powers 2013 Cambridge University Press Field diagrams Field diagrams are used to calculate the area of irregularly shaped blocks of land. A traverse survey measures distances along a suitable diagonal or traverse. HSC Hint – Measurements on the traverse always start at the bottom. 6

 G K Powers 2013 Cambridge University Press Volume of prisms and cylinders Volume is the amount of space occupied by a three- dimensional object. HSC Hint – Volume of all prisms are calculated by multiplying the area of the base by the height. 7

 G K Powers 2013 Cambridge University Press Capacity The capacity of a container is the amount of liquid it can hold. Some solids have both a volume and a capacity. 1 ML = kL 1 ML = L 1 kL = 1000 L 1 L = mL 1 cm 3 = 1 mL 1 cm 3 = L 1000 cm 3 = 1 L 1 m 3 = cm 3 1 m 3 = mL 1 m 3 = L 1 m 3 = 1 kL HSC Hint – Learn the above unit conversions. The most common conversion is 1 cm 3 = 1 mL. 8