11+ Area and Perimeter: Questions with Worked Answers

Imagine buying a floor covering and a strip of edging for the same room. The floor covering depends on how much surface there is; the edging depends on the distance around the boundary. Those are different measurements, even though both start from the same shape. Naming the measurement before calculating is the first useful check.

These original explanations and questions support preparation for 11-plus exams taken in 2027. They are not an official paper or a promise that every school tests these topics. Use your target school’s current guidance, and try each question before opening its worked answer.

Choose the measurement, then the units

Area measures surface in square units, such as cm² or m². Perimeter measures a boundary in length units, such as cm or m. For a rectangle, area is length × width and perimeter is 2 × (length + width). Both dimensions must use the same unit before you use either formula. A square is a rectangle whose four sides are equal.

These rectangles have the same perimeter and different areas. Knowing only a rectangle’s perimeter does not normally determine its area. Sketch both examples and label all four sides: this makes the difference visible without relying on the formula names.

Work backwards from what is known

A rectangular display has area 84 cm² and width 7 cm. Divide 84 by 7 to find its length, 12 cm. If instead you know the perimeter is 38 cm and one side is 8 cm, halve the perimeter to get length + width = 19 cm, then subtract 8 to obtain 11 cm. Do not divide the full perimeter by the known side.

Handle a missing corner without inventing a diagram

Suppose a 14 m by 9 m rectangle has a 5 m by 3 m rectangle removed from its top-right corner, with the removed edges along the outside boundary. Its area is 126 − 15 = 111 m². Trace the new boundary: the two removed outer lengths are replaced by equal lengths along the notch. Its perimeter remains 46 m. That perimeter shortcut applies to this corner removal, not every possible hole or indentation.

For mixed units, convert before multiplying: a panel 1.4 m long and 60 cm wide is 140 cm by 60 cm, so its area is 8,400 cm². A square metre contains 100 × 100 square centimetres. Converting an area therefore uses a different factor from converting a length.

Eight questions: write the unit too

Check the last step

Ask whether the question wants a measurement or a cost based on that measurement. A correct perimeter is only an intermediate answer if a gate must be removed or a price applied. When an answer looks plausible, check its unit: a length cannot be the area of the floor.

Return to the Maths learning hub, choose original practice and print resources, or continue with multi-step word problems. When reviewing, record the step you missed rather than just copying the answer. Explain one corrected question aloud, then try a different example of the same skill.

Teaching context checked 25 October 2026: DfE maths programme. This is curriculum context, not a school-specific exam specification. The examples, questions and explanations here are original; no official mark scheme or qualified-educator review is claimed.