Sec 1 · G3 (Express)

Perimeter and area

Practise perimeter and area with step-by-step help. Free account.

1. Area formulae

Drawn to scale: a parallelogram with base 9, slant side 5 and perpendicular height 4, area 36; a trapezium with parallel sides 6 and 10 and height 5, area 40; an obtuse triangle with base 6 whose height 4 falls outside it, area 12; a circle with radius r.

Shape	Area	Perimeter
rectangle	$l \times b$	$2(l + b)$
square	$l^{2}$	$4l$
triangle	$\dfrac{1}{2} \times b \times h$	add the sides
parallelogram	$b \times h$	add the sides
trapezium	$\dfrac{1}{2}(a + b) \times h$	add the sides
circle	$\pi r^{2}$	$2\pi r$

📖 Worked example

In the diagram, $ABCD$ is a trapezium with $AB$ parallel to $DC$ . The dashed line is perpendicular to $AB$ . Find the area of $ABCD$ .

Step 1 of 1

Add the two PARALLEL sides, then use the perpendicular height (dashed)

\text{Area of } ABCD = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}

= \dfrac{1}{2} \times (9 + 24) \times 9

= 148.5

cm²

Practise this →

2. Circles and semicircles

Circle, radius 7 cm: keep π, round once at the end

\displaystyle A = \pi r^{2}

e.g.

\displaystyle \pi(7)^{2}

\displaystyle = 49\pi

\displaystyle = 154\text{ (3 s.f.)}

Perimeter of a semicircle, radius 7 cm: the arc and the diameter

\displaystyle \dfrac{1}{2}(2\pi r) + 2r

e.g.

\displaystyle \pi(7) + 14

\displaystyle = 36.0\text{ (3 s.f.)}

📖 Worked example

The diagram shows a circular garden pond. Its diameter is $16$ m. Find its circumference, leaving your answer in terms of $\pi$ .

Step 1 of 2

The radius is half the diameter

r = \dfrac{16}{2}

= 8

📖 Worked example

The diagram shows a semicircle of diameter $24$ cm. Find its perimeter, correct to 3 significant figures.

Step 1 of 3

The radius is half the diameter

r = \dfrac{24}{2}

= 12

Practise this →

3. Composite figures

Split into rectangles, or take the missing part away

\displaystyle 10 \times 6 - 6 \times 3

e.g.

\displaystyle 10 \times 6 - 6 \times 3

\displaystyle = 42

an L-shape: a $10$ by $6$ rectangle with a $6$ by $3$ corner cut out

📖 Worked example

The diagram shows a figure made up of rectangles. All the corners are right angles. Find its area.

Step 1 of 2

Split the figure into two rectangles and find the missing side

\text{Missing side} = 18 - 11

= 7

📖 Worked example

The diagram shows a hexagon made of two identical trapeziums joined along their longer parallel sides (the dashed line). The parallel sides of each trapezium are $4$ cm and $10$ cm. The area of the hexagon is $42$ cm². Find the value of $h$ .

Step 1 of 2

The two trapeziums are identical: each is half the hexagon

\text{One trapezium} = \dfrac{42}{2}

\phantom{\text{One trapezium}} = 21

cm²

📖 Worked example

The diagram shows two circles with the same centre $O$ , of radii $3$ cm and $5$ cm. The shaded ring between them is divided into $2$ parts of equal area by a dashed circle, also with centre $O$ . Find the radius, $r$ cm, of the dashed circle.

Step 1 of 4

Area of the shaded ring = big circle − small circle

\text{Ring} = \pi(5)^2 - \pi(3)^2

= 16\pi

cm²

Practise this →

4. Units of area

Length	Area
$1\text{ m} = 100\text{ cm}$	$1\text{ m}^{2} = 10\,000\text{ cm}^{2}$
$1\text{ cm} = 10\text{ mm}$	$1\text{ cm}^{2} = 100\text{ mm}^{2}$
	$1\text{ ha} = 10\,000\text{ m}^{2}$

📖 Worked example

The floor of a kitchen is a rectangle measuring $6$ m by $4.2$ m. It is covered completely with square tiles of side $60$ cm. Find the number of tiles needed.

Step 1 of 3

Change the floor's lengths to centimetres

6 \text{ m} = 600 \text{ cm}

4.2 \text{ m} = 420 \text{ cm}

Practise this →

Try a question: Perimeter and area

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Practise perimeter and area with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

Start free

Practice questions by skill

Sec 1 · G3 (Express)

Perimeter and area

Practise perimeter and area with step-by-step help. Free account.

Start free Worksheet (PDF)

1. Area formulae

Shape	Area	Perimeter
rectangle	$l \times b$	$2(l + b)$
square	$l^{2}$	$4l$
triangle	$\dfrac{1}{2} \times b \times h$	add the sides
parallelogram	$b \times h$	add the sides
trapezium	$\dfrac{1}{2}(a + b) \times h$	add the sides
circle	$\pi r^{2}$	$2\pi r$

📖 Worked example

In the diagram, $ABCD$ is a trapezium with $AB$ parallel to $DC$ . The dashed line is perpendicular to $AB$ . Find the area of $ABCD$ .

Step 1 of 1

Add the two PARALLEL sides, then use the perpendicular height (dashed)

\text{Area of } ABCD = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}

= \dfrac{1}{2} \times (9 + 24) \times 9

= 148.5

cm²

Practise this →

2. Circles and semicircles

Circle, radius 7 cm: keep π, round once at the end

\displaystyle A = \pi r^{2}

e.g.

\displaystyle \pi(7)^{2}

\displaystyle = 49\pi

\displaystyle = 154\text{ (3 s.f.)}

Perimeter of a semicircle, radius 7 cm: the arc and the diameter

\displaystyle \dfrac{1}{2}(2\pi r) + 2r

e.g.

\displaystyle \pi(7) + 14

\displaystyle = 36.0\text{ (3 s.f.)}

📖 Worked example

The diagram shows a circular garden pond. Its diameter is $16$ m. Find its circumference, leaving your answer in terms of $\pi$ .

Step 1 of 2

The radius is half the diameter

r = \dfrac{16}{2}

= 8

📖 Worked example

The diagram shows a semicircle of diameter $24$ cm. Find its perimeter, correct to 3 significant figures.

Step 1 of 3

The radius is half the diameter

r = \dfrac{24}{2}

= 12

Practise this →

3. Composite figures

Split into rectangles, or take the missing part away

\displaystyle 10 \times 6 - 6 \times 3

e.g.

\displaystyle 10 \times 6 - 6 \times 3

\displaystyle = 42

an L-shape: a $10$ by $6$ rectangle with a $6$ by $3$ corner cut out

📖 Worked example

The diagram shows a figure made up of rectangles. All the corners are right angles. Find its area.

Step 1 of 2

Split the figure into two rectangles and find the missing side

\text{Missing side} = 18 - 11

= 7

📖 Worked example

Step 1 of 2

The two trapeziums are identical: each is half the hexagon

\text{One trapezium} = \dfrac{42}{2}

\phantom{\text{One trapezium}} = 21

cm²

📖 Worked example

Step 1 of 4

Area of the shaded ring = big circle − small circle

\text{Ring} = \pi(5)^2 - \pi(3)^2

= 16\pi

cm²

Practise this →

4. Units of area

Length	Area
$1\text{ m} = 100\text{ cm}$	$1\text{ m}^{2} = 10\,000\text{ cm}^{2}$
$1\text{ cm} = 10\text{ mm}$	$1\text{ cm}^{2} = 100\text{ mm}^{2}$
	$1\text{ ha} = 10\,000\text{ m}^{2}$

📖 Worked example

The floor of a kitchen is a rectangle measuring $6$ m by $4.2$ m. It is covered completely with square tiles of side $60$ cm. Find the number of tiles needed.

Step 1 of 3

Change the floor's lengths to centimetres

6 \text{ m} = 600 \text{ cm}

4.2 \text{ m} = 420 \text{ cm}

Practise this →

Try a question: Perimeter and area

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Practise perimeter and area with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

Start free