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

The Eduqas geometry content asks you to find the area and perimeter of standard 2D shapes (rectangles, triangles, parallelograms, trapezia, circles and sectors), and the surface area and volume of 3D solids (prisms, cylinders, pyramids, cones and spheres). Measurement is one of the most heavily tested areas, mixing formula recall with multi-step problem solving. Some formulae are given on the Eduqas list (the sphere and cone), while others must be recalled (rectangle, triangle, circle), so knowing which is which, and when to use each, is essential. It runs across both tiers and both components.

Area and perimeter of 2D shapes

Each common shape has an area formula, and the perimeter is the total distance around the edge.

So a trapezium with parallel sides $6$ cm and $10$ cm and perpendicular height $4$ cm has area $\tfrac{1}{2}(6 + 10) \times 4 = 32$ cm squared. A compound shape (an L-shape, say) is split into rectangles whose areas are added. The perpendicular height is the recurring trap: in a triangle or parallelogram you must use the height at right angles to the base, not a sloping edge.

Circles and sectors

The circle formulae are core knowledge and must be recalled.

The most common slip is confusing area ($\pi r^2$) with circumference ($2\pi r$), or using the diameter where the formula needs the radius. A sector is simply the fraction $\dfrac{\theta}{360}$ of the whole circle, so a quarter circle ($90^\circ$) has a quarter of the area and a quarter of the circumference as its arc.

Volume of 3D solids

Volume measures the space inside a solid, and a prism's volume follows one general rule.

For the curved solids, the cylinder is $\pi r^2 h$, the sphere is $\tfrac{4}{3}\pi r^3$ and the cone is $\tfrac{1}{3}\pi r^2 h$; the sphere and cone formulae are given on the Eduqas list, so use them directly.

Surface area

Surface area is the total area of all the faces of a solid, so a systematic count of every face prevents omissions. A cuboid has six rectangular faces in three matching pairs. A cylinder has two circular ends ($2\pi r^2$) plus a curved surface that unrolls into a rectangle of area $2\pi r h$. A cone has a circular base ($\pi r^2$) plus a curved surface $\pi r l$, where $l$ is the slant height (found by Pythagoras from $r$ and the vertical height). Listing the faces before adding is the reliable method, and Eduqas often leaves answers in terms of $\pi$ on the non-calculator paper.

Units and why measurement matters

Keeping units straight is half the battle in measurement questions. Length is measured in single units (cm), area in square units (cm squared) because it is length times length, and volume in cubic units (cm cubed) because it is length times length times length. This also governs conversions: $1$ m $= 100$ cm, so $1$ m squared $= 100^2 = 10000$ cm squared and $1$ m cubed $= 100^3 = 1000000$ cm cubed, a point Eduqas tests directly. Measurement underpins a great deal of real mathematics, from packaging and construction to the capacity of containers, and it connects to the compound-measures work where volume feeds into density. Because these questions reward a clear method, always write the formula, substitute with units, and state the unit of the answer.