Geometry
What this domain tests
Geometry covers scale drawings, angle relationships, circumference and area of circles, and area, surface area, and volume of two- and three-dimensional figures. Expect composite figures and multi-step problems involving π.
Core rules
- Scale factor compares corresponding lengths; areas scale by the square of the scale factor.
- Angles on a straight line sum to 180°; angles around a point sum to 360°; vertical angles are equal.
- Circle: C = 2πr = πd and A = πr².
- Volume of a right prism: V = Bh, where B is the base area. Volume of a cylinder: V = πr²h.
- Surface area is the sum of all face areas; use a net to avoid missing a face.
Worked example
A circle has diameter 10 cm, so r = 5 cm. Circumference = 2π(5) = 10π ≈ 31.4 cm. Area = π(5²) = 25π ≈ 78.5 cm². Keeping π in the answer until the end avoids rounding error.
Composite figure: a rectangle 10 m by 6 m with a semicircle of diameter 6 m attached to one 6 m side. Rectangle area = 60 m². Semicircle radius = 3 m, area = ½π(3²) = 4.5π ≈ 14.1 m². Total ≈ 74.1 m². The straight edge of the semicircle is shared, so it is not added to the perimeter.
Traps that cost marks
- Using the diameter in A = πr².
- Confusing circumference, a length, with area, measured in square units.
- Scaling area by the scale factor instead of its square.
- Adding the shared edge twice in composite perimeter problems.
- Rounding π to 3 too early and losing accuracy.