Geometry and Spatial Calculations

Geometry questions in the UCAT Quantitative Reasoning subtest test your ability to calculate areas, perimeters, volumes, and surface areas. You may also encounter questions involving scale drawings, map calculations, and spatial reasoning. The formulas you need will usually be provided — the challenge is applying them correctly under time pressure.

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Areas and Perimeters of Common Shapes

Rectangle

Measure	Formula
Area	length × width
Perimeter	2 × (length + width)

Triangle

Measure	Formula
Area	(1/2) × base × height
Perimeter	sum of all three sides

Important: The "height" must be the perpendicular height — the vertical distance from the base to the opposite vertex. It is NOT always one of the sides of the triangle.

Circle

Measure	Formula
Area	pi × r²
Circumference	2 × pi × r (or pi × d)

Where r = radius, d = diameter = 2r, and pi ≈ 3.14159

Trapezium