Geometry and Measurement
Geometry and Measurement
Candidates need angle properties, triangle and polygon facts, circle formulas, area, perimeter, surface area, volume, similarity, congruence, the Pythagorean theorem, and coordinate geometry. Know that the angles in a triangle sum to 180°, that corresponding angles are equal in similar figures, and that scale factors apply differently to lengths, areas, and volumes. Convert units carefully before calculating.
Traps: confusing radius with diameter; using slant height instead of perpendicular height; double-counting shared edges in composite figures; and mixing units such as cm and m. In similarity, if the length scale factor is k, areas scale by k² and volumes by k³. A common error is assuming two triangles are congruent when only their angles match. For circles, check whether the question asks for circumference or area. For volume, ensure all dimensions are in the same unit.
Rule of thumb: sketch and label the figure, write the formula first, then substitute. For composite shapes, add or subtract simple areas deliberately rather than guessing.
Worked example: a circle has diameter 10 cm. Its radius is 5 cm, so area = πr² = 25π cm² ≈ 78.5 cm². Circumference = πd = 10π cm ≈ 31.4 cm. Notice that the area answer is in square centimetres, while circumference is in centimetres.