IGCSE · Practice questions · Area and perimeter of 2D shapes

Formulas you must know.

Six original Cambridge-style questions on the perimeter and area of rectangles, triangles, parallelograms and trapezia, including working backwards from an area.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Perpendicular height, every time.

Rectangle: $A = lw$.
Triangle: $A = \tfrac{1}{2}bh$ (the only one given in the exam).
Parallelogram: $A = bh$.
Trapezium: $A = \tfrac{1}{2}(a+b)h$, $a$ and $b$ parallel.
Perimeter: add every side, including the sloping ones.
Backwards: substitute what you know and solve for the missing length.

Recall

[2 marks]

A rectangle measures 9.5 cm by 4 cm. Find (a) its area (b) its perimeter.

(a) $9.5 \times 4 = 38\text{ cm}^2$ ✓
(b) $2(9.5 + 4) = 27$ cm ✓

Calculation

[2 marks]

Find the area of (a) a triangle with base 11 cm and perpendicular height 8 cm (b) a parallelogram with base 7.5 cm and perpendicular height 4 cm.

(a) $\tfrac{1}{2} \times 11 \times 8 = 44\text{ cm}^2$ ✓
(b) $7.5 \times 4 = 30\text{ cm}^2$ ✓

Calculation

[2 marks]

Without a calculator, find the area of a trapezium with parallel sides 4.6 cm and 7.4 cm, a distance of 3.5 cm apart.

$4.6 + 7.4 = 12$, and half of 12 is 6. ✓
$6 \times 3.5 = 21\text{ cm}^2$ ✓

Analysis

[3 marks]

A rectangle measures 16 cm by 9 cm. A square has the same area as the rectangle.

Find the difference between the perimeters of the rectangle and the square.

Area $= 16 \times 9 = 144\text{ cm}^2$, so the square has side $\sqrt{144} = 12$ cm. ✓
Perimeters: rectangle $2(16 + 9) = 50$ cm, square $4 \times 12 = 48$ cm. ✓
Difference $= 50 - 48 = 2$ cm. ✓

Analysis

[3 marks]

A trapezium has area $72\text{ cm}^2$. The distance between its parallel sides is 8 cm, and one of the parallel sides is 7 cm long.

Find the length of the other parallel side.

$72 = \tfrac{1}{2}(7 + b) \times 8 = 4(7 + b)$. ✓
$7 + b = 18$. ✓
$b = 11$ cm. ✓

Analysis

[4 marks]

A garden is a trapezium. Its parallel sides are 12 m and 18 m long and they are 9 m apart.

Turf is sold only in whole square metres at $6.40 per square metre. The gardener orders 10% more turf than the area of the garden, to allow for waste.

Calculate the cost of the turf.

Area $= \tfrac{1}{2}(12 + 18) \times 9 = 135\text{ m}^2$. ✓
Add 10%: $135 \times 1.1 = 148.5\text{ m}^2$. ✓
Whole square metres, and at least 148.5 is needed, so buy $149\text{ m}^2$. ✓
Cost $= 149 \times 6.40 = \$953.60$. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.