courses › Geometry

Area & perimeter

level 17 course

Rectangles, triangles, trapezoids, and shapes made of them.

In your head, jot if needed · no calculator why?

Opens at level 17.

Builds on: Bigger multiplication (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Area is the space a flat shape covers, counted in squares: square metres, square feet. Perimeter is the distance around the edge, in plain metres or feet.

Rectangles are the base case: area is length × width. A triangle is half of a rectangle with the same base and height. A trapezoid, a four-sided shape with one pair of parallel sides, works like a rectangle whose width is the average of those two sides. Bigger shapes break into these pieces.

Techniques

Rectangle: multiply or go around

Any rectangle.

Area: length × width, in square units.
Perimeter: add all four sides, which is 2 × (length + width).

worked example

Example: A rectangle is 12 m by 7 m. What is its perimeter in metres?

2 × (12 + 7) = 2 × 19 = 38 m.
Its area would be 12 × 7 = 84 square metres.

Answer: 38

Halve for triangles and trapezoids

Triangles, and four-sided shapes with one pair of parallel sides.

Triangle: base × height ÷ 2. The height is measured at a right angle to the base.
Trapezoid: add the two parallel sides, halve, then multiply by the height.

worked example

Example: A trapezoid has parallel sides of 6 cm and 10 cm and a height of 4 cm. What is its area in square centimetres?

Average the parallel sides: (6 + 10) ÷ 2 = 8.
Multiply by the height: 8 × 4 = 32 cm².

Answer: 32

Break it into rectangles

L-shapes and other shapes made of rectangles.

A corner cut out: the whole rectangle minus the missing piece.
Two rectangles joined: add their areas.
Sketch it and label every length before you multiply.

worked example

Example: A patio is a 9 m × 6 m rectangle with a 3 m × 2 m corner cut out. What is its area in square metres?

Whole rectangle: 9 × 6 = 54.
Missing corner: 3 × 2 = 6.
54 − 6 = 48 m².

Answer: 48

Tips by skill

TipRectangles: Area multiplies length by width. Perimeter goes around: twice the length plus twice the width.
TipTriangles & trapezoids: Triangle: half of base × height. Trapezoid: average the parallel sides, then multiply by the height.
TipComposite shapes: Corner cut out? Subtract its area from the whole rectangle. Two rectangles joined? Add their areas.

Watch out for

Giving the perimeter when the question asks for area, or the reverse. Square metres means area.
Forgetting to halve for a triangle or a trapezoid.
Adding the cut-out corner instead of subtracting it.
Adding only two sides for a perimeter. A rectangle has four.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

Rectangles par 10 s not tried yet
worked example
A rectangle is 6 ft by 14 ft. What is its perimeter in feet?

Answer: 40
1. Perimeter = 2 × (6 + 14) = 2 × 20 = 40 ft.
Triangles & trapezoids par 16 s not tried yet
worked example
A triangle has a base of 28 cm and a height of 7 cm. What is its area in square centimetres?

Answer: 98
1. Area = ½ × base × height = ½ × 28 × 7 = 98 cm².
Composite shapes par 25 s not tried yet
worked example
An L-shaped garden is a 15 ft × 20 ft rectangle with a 3 ft × 6 ft corner cut out. What is its area in square feet?

Answer: 282
1. Whole rectangle minus the missing corner: 15 × 20 − 3 × 6 = 300 − 18 = 282 ft².

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1 day
3 days
7 days
14 days
30 days
60 days
mastered · every 90 days

your rounds

No rounds yet.