Calculate the area and perimeter of rectangles, triangles, parallelograms, trapezia, circles and sectors; and the surface area and volume of prisms, cylinders, pyramids, cones and spheres.

What this dot point is asking

OCR references G16, G17 and G18 cover area and perimeter of 2D shapes (including circles and sectors) and surface area and volume of 3D solids (prisms, cylinders, pyramids, cones and spheres). Mensuration is a core, heavily examined topic on every tier. Some formulae must be recalled (rectangle, triangle, circle, prism), while the more complex ones (sphere, cone) are given on the OCR formulae sheet, so knowing which is which, and how to use each, matters.

Area and perimeter of 2D shapes

The standard area formulae cover the common polygons.

The height in the triangle and parallelogram formulae is the perpendicular height, not a slant side. For a composite shape, split it into known shapes, find each area, then add (or subtract a cut-out). Perimeter is found by adding every side; for a composite shape, take care to include only the outer edges.

Circles and sectors

Circles have their own two key formulae.

So a circle of radius $6$ has area $36\pi \approx 113.1$ and circumference $12\pi \approx 37.7$. A sector with angle $90^\circ$ is a quarter circle, so its area is $\tfrac{1}{4}\pi r^2$. The circle area must be recalled; mixing up the area $\pi r^2$ with the circumference $2\pi r$ is one of the most common slips in the whole subject.

Surface area and volume of 3D solids

Volume measures the space inside; surface area measures the total outer area.

Surface area is found by adding the areas of every face. For a cylinder, that is two circles ($2\pi r^2$) plus the curved surface ($2\pi r h$). For a cone it is the base ($\pi r^2$) plus the curved surface ($\pi r l$, where $l$ is the slant height). Building the surface area face by face, and labelling each piece, keeps long calculations organised.

Why mensuration matters

Area and volume appear in packaging, construction, capacity and density problems, and OCR links them to compound measures and to ratio (areas scale by the square of a length factor, volumes by the cube). Recalling the core formulae and selecting the given ones correctly, then keeping units consistent (and squared or cubed), is exactly what the marks reward. Leaving an answer "in terms of $\pi$" when asked keeps it exact.