Vocabulary: (as for MM1) accuracy adjacent angle of depression angle of elevation area capacity composite figure cosine ratio cylinder error  field diagram hypotenuse opposite perimeter quadrant rate ratio right prism scale diagram scale factor scientific notation significant figures similar sine ratio standard prefix tangent ratio trigonometry unitary method volume

Basic Concepts: calculate the perimeter of simple figures, including right-angled triangles, circles, semicircles and quadrants calculate the perimeter and area of simple composite figures consisting of two shapes, including semicircles and quadrants calculate the perimeter and area of irregularly shaped blocks of land using a field diagram identify and use the correct formula to solve practical area problems calculate the volume of right prisms and cylinders using appropriate formulae estimate areas and volumes convert between units of volume and capacity.

Perimeter

Perimeter of Circles This is also called the ‘circumference’.

Area of Simple Figures

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Field diagrams Surveyors are often required to draw scale diagrams and to calculate the area of irregularly shaped blocks of land. This is done using a traverse survey. In this survey, a diagonal (traverse) is constructed between two corners of the block. The diagonal is then measured. From this diagonal each other corner is sighted at right angles to the diagonal. Each of these lines, called an offset, is measured. These offsets then divide the block into triangles and quadrilaterals, hence we can calculate the area. The results of a traverse survey are displayed in a field diagram.

Field diagrams This is a field diagram for a specific area: This is the field diagram drawn as a scale diagram using geogebra:

A typical problem in this unit is to find the area and perimeter of a field. We find the area of each section, then adding all answers together to get the area. For perimeter, add the sections on the outside of the diagram and adding them together. Find the AREA of this field:

To find the perimeter, you will generally need to use Pythagoras' Theorem for each triangle.

Volumes of Prisms and Cylinders

Conversion between Units

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