Geometry and Mensuration
Geometry and mensuration
This domain covers angle facts, properties of triangles and quadrilaterals, parallel-line angles, polygons, congruence and similarity, Pythagoras theorem, circle vocabulary, and area, perimeter, surface area and volume. You must calculate angles in triangles, straight lines, at a point and in polygons; use the interior angle sum (n - 2) x 180 degrees; and apply similarity scale factors. Mensuration includes rectangles, triangles, parallelograms, trapezia, circles, prisms, cylinders and composite shapes.
Frequent traps are using the diameter instead of the radius, mixing units such as cm and m, and forgetting that area and volume scale differently under enlargement. If lengths are enlarged by scale factor k, areas scale by k^2 and volumes by k^3. For composite shapes, split them into standard parts and add or subtract areas. In circle work, circumference = 2 pi r and area = pi r^2; do not interchange them. Check whether a question asks for exact answers in terms of pi or a numerical value.
Worked example: a circle has radius 7 cm. Area = pi r^2 = pi x 7^2 = 49 pi, approximately 154 cm^2 using pi = 22/7. Circumference = 2 pi r = 14 pi, approximately 44 cm. The diameter is 14 cm, not 7 cm.
Rule of thumb: write the formula, substitute the given values with units, then calculate; this reduces the chance of using the wrong measurement.