Papy

Area and Perimeter - Edexcel GCSE Higher Maths

Typically 4-7 marks per paper, from a two-mark formula question to a full problem-solving question · Spec 1MA1

Two spec references carry this topic on Edexcel's 1MA1. G16 asks you to know and apply the formulae for the area of a triangle, a parallelogram and a trapezium. G17 adds the circumference and area of a circle, the perimeter of a 2D shape including one with a curved edge, and the area of a composite shape. None of that is Higher only, so a Foundation candidate meets every formula on the list. What changes at Higher is the packaging: you are handed an area and asked for a missing length, or a figure described purely by the coordinates of its vertices, or a shape whose area is step one of a four-step costing problem.

The Higher Tier Exam Aid issued with the 1MA1 papers for the 2025, 2026 and 2027 assessment windows prints three of the formulae used here: area of a trapezium as 12(a+b)h\frac{1}{2}(a + b)h, where aa and bb are the parallel sides and hh is their perpendicular separation, circumference of a circle as 2πr2\pi r or πd\pi d, and area of a circle as πr2\pi r^2. The sheet's only triangle entry is the area rule, 12absin⁡C\frac{1}{2}ab\sin C, which needs two sides and the angle between them; half the base times the perpendicular height is not there, nor is the area of a parallelogram, and nothing on it tells you how to handle a compound shape. The topic can appear on any of the three papers. Papers 2 and 3 allow a calculator and come with a rounding instruction, normally 1 decimal place or 3 significant figures. On Paper 1 the circle numbers are chosen so the answer stays as a multiple of π\pi, and a semicircle of radius 8 cm has area 32π32\pi cm2^2 full stop, with no decimal to follow.

Most of the dropped marks come from three places. The first is answering the other question: giving an area where a perimeter was asked for, or building the perimeter of an L-shape by adding the perimeters of the two rectangles it splits into, which counts the join twice and inflates the answer. The second is the radius and diameter swap, which turns π×72\pi \times 7^2 into π×142\pi \times 14^2 and makes a circle four times too big. The third is units, where a 2.5 m by 1.8 m rectangle is converted to 4.5 cm2^2 instead of 45 000 cm2^2, because each metre carries a factor of 100 and there are two lengths. On a costing question the final mark is usually for rounding up to a whole number of tins or bags, so a script that reaches 3.85 and stops has done all the mathematics and none of the answering.

Worked example

The floor of a hallway is a trapezium. The two parallel walls are 6.4 m and 4.6 m long, and the perpendicular distance between them is 3.5 m. Floor varnish is sold in tins. One tin covers 5 m2^2 of floor. A tin of varnish costs £18.95. Work out the total cost of the varnish needed to cover the floor.
[5 marks]
  1. Substitute the two parallel sides and the perpendicular distance into the trapezium formula: area =12×(6.4+4.6)×3.5= \frac{1}{2} \times (6.4 + 4.6) \times 3.5.
    M1: correct substitution into the formula printed on the Exam Aid; the parallel sides are added first, then halved
  2. 12×11×3.5=19.25\frac{1}{2} \times 11 \times 3.5 = 19.25, so the floor area is 19.25 m2^2.
    A1: 19.25 m2^2; a candidate who multiplies 6.4 by 4.6 has treated the trapezium as a rectangle
  3. Each tin covers 5 m2^2, so divide: 19.25÷5=3.8519.25 \div 5 = 3.85 tins.
    M1: dividing their area by 5, awarded even if the area is wrong
  4. Tins are only sold whole, so 3.85 rounds up to 4 tins.
    M1: rounding up rather than to the nearest whole number; 3.85 rounded to 4 by accident still scores, but 3 does not
  5. Cost =4×18.95=75.80= 4 \times 18.95 = 75.80, so the varnish costs £75.80.
    A1: £75.80, written with two decimal places because it is money

Practice questions

These are original questions written in Edexcel 1MA1 Higher style. There are no diagrams, so every shape is described in words: read whether a length is a radius or a diameter, and whether a height is perpendicular or slanted, before you substitute. Where a question says the answer is kπk\pi, type the value of kk only, and where it states a rounding, keep the full calculator display until the last line.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

  1. Question 1 Warm-up [2 marks]
    A semicircle has a radius of 8 cm. The area of the semicircle is kπk\pi cm2^2. Write down the value of kk.
  2. Question 2 Warm-up [2 marks]
    A quadrant of a circle has a radius of 12 cm. The area of the quadrant is kπk\pi cm2^2. Write down the value of kk.
  3. Question 3 Exam pace [3 marks]
    A trapezium has vertices at the points A(0, 0), B(10, 0), C(7, 5) and D(2, 5). Work out the area of the trapezium, in square units.
  4. Question 4 Stretch [4 marks]
    A rectangle has a perimeter of 46 cm. Its length is 5 cm more than its width. Work out the area of the rectangle, in cm2^2.
  5. Question 5 Stretch [4 marks]
    A running track is made from a rectangle 80 m long and 50 m wide, with a semicircle joined to each of the two 50 m ends. Each semicircle has a 50 m side of the rectangle as its diameter. Work out the perimeter of the track, in m, correct to 1 decimal place.
  6. Question 6 Stretch [4 marks]
    A piece of wire 60 cm long is bent to form a circle. Work out the area enclosed by the circle, in cm2^2, correct to the nearest whole number.

Common mistakes examiners see

  • Finding the perimeter of a compound shape by adding the perimeters of the pieces. An L-shape cut from a 14 m by 9 m rectangle by removing a 5 m by 4 m corner is answered as 46 plus 18, or as the sum of two rectangle perimeters, when the true perimeter is 46 m.

    Trace the outline with your finger, starting at one corner and counting the sides as you go, and only include edges you actually walk along. For a rectangle with a corner cut out the perimeter is unchanged, because the two new edges replace exactly the lengths they removed. That check takes five seconds and catches the doubling.

  • Using a sloping side as the height. A trapezium with parallel sides 7 cm and 13 cm, sloping sides of 5 cm and a perpendicular separation of 4 cm gives 12×20×5=50\frac{1}{2} \times 20 \times 5 = 50 cm2^2 instead of 40 cm2^2.

    The hh in the printed formula is the perpendicular distance between the parallel sides, never the slant. Underline the word perpendicular in the question, and if a triangle or trapezium hands you three lengths, expect one of them to be the decoy that Pythagoras would link to the other two.

  • Putting the diameter into πr2\pi r^2. A circle of diameter 14 cm gives π×142=196π\pi \times 14^2 = 196\pi rather than π×72=49π\pi \times 7^2 = 49\pi, an answer four times too large.

    Write r=…r = \ldots on its own line before substituting anything, halving the diameter there. The mirror error is doubling a radius that was already a radius in πd\pi d, so decide which letter you have been given before you pick between 2πr2\pi r and πd\pi d.

  • Giving the perimeter of a semicircle as just the curved part. A semicircle of diameter 14 cm answered as 12×π×14=22.0\frac{1}{2} \times \pi \times 14 = 22.0 cm has left out the straight edge; the perimeter is 36.0 cm to 1 decimal place.

    A semicircle has two edges, an arc and a diameter, and a quadrant has three, an arc and two radii. Count the edges before you calculate, and add the straight ones back in. Area questions on the same shapes need only the fraction of the circle, which is why the two are easy to confuse under time pressure.

  • Converting an area with the length conversion factor: writing 4.5 m2^2 as 450 cm2^2, or 3 m2^2 as 300 cm2^2.

    Convert the lengths first, then multiply. A 2.5 m by 1.8 m rectangle is 250 cm by 180 cm, so 45 000 cm2^2. If you would rather convert at the end, the factor for areas is 1002100^2, which is 10 000, from m2^2 to cm2^2, and 102=10010^2 = 100 from cm2^2 to mm2^2.

Frequently asked questions

Is the area of a trapezium formula given in the Edexcel GCSE maths exam?
Yes. For the 2025, 2026 and 2027 assessment windows the Higher Tier Exam Aid is issued as an insert with every 1MA1 paper, and it gives the area of a trapezium as half of (a+b)(a + b) multiplied by hh, along with the circumference and area of a circle. Half the base times the perpendicular height is not on it, and neither is the area of a parallelogram, so those two stay in your memory. The sheet does carry 12absin⁡C\frac{1}{2}ab\sin C, but that is the area rule for a triangle given two sides and the angle between them, which is a different question.
Is area and perimeter on the Foundation paper as well as Higher?
Yes, all of it. G16 and G17 are common content, so the same formulae are examined at both tiers. The difference is how far the question travels: a Higher paper is far more likely to give you the area and ask for a missing side, to describe the shape only by its coordinates, or to bury the area inside a costing or comparison problem worth 4-5 marks.
How do you find the perimeter of a semicircle?
Halve the circumference of the full circle and then add the diameter, because the straight edge is part of the boundary. For a semicircle of diameter 14 cm that is π×14÷2=21.99\pi \times 14 \div 2 = 21.99 cm of arc plus 14 cm of diameter, giving 36.0 cm to 1 decimal place. Leaving out the diameter is the single most common way this question is lost.
How many marks is area and perimeter worth on Edexcel Higher?
A single formula question is usually 2-3 marks and sits early in the paper. A compound shape, a reverse question that starts from the area, or a problem that ends in a cost or a number of bags runs to 4-5 marks. Across an 80-mark paper expect roughly 4-7 marks, and area also turns up inside other topics, most often when a prism volume needs its cross section first.

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