Perimeter of a Polygon
The perimeter of a polygon is the total length of all its sides. To find the perimeter, add up the length of every side: a triangle with sides of 5, 4 and 3 cm has a perimeter of 12 cm. For a rectangle, use the shortcut 2 × (length + width).
Video Lesson
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Flashcards
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What is Perimeter?
- The perimeter of a polygon is the total length of its boundary.
- For a rectangle: length + width).
- For a square: side length.
Perimeter of Triangles
- The perimeter of a triangle is the sum of its three sides.
- For an isosceles triangle: equal side + base
- For an equilateral triangle: side length
Perimeter of Complex Shapes
- Add the lengths of the edges around the outside of the shape.
- You can also add lengths together to think of the shape as a rectangle.
Practice Questions
Test your understanding
What is the perimeter of a square with side length ?
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All four sides of a square are the same length, so the perimeter is
.
Perimeter is the distance all the way round the edge, so the answer is measured in cm, not cm².
Find the perimeter of a rectangle with length and width .
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A rectangle has two lengths and two widths, so the perimeter is
.
You can also add the four sides one at a time: cm.
The perimeter of an equilateral triangle is . What is the length of one side?
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An equilateral triangle has three equal sides, so the perimeter is . To reverse this, divide by 3:
.
Check: cm.
An isosceles triangle has a base of and two equal sides of each. What is its perimeter?
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The perimeter is the total distance round the outside, so add all three sides. The side appears twice:
.
An irregular hexagon has edges of the following lengths: , , , , , and . What is its perimeter?
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The perimeter is the sum of all six edge lengths:
.
Ticking each length off as you add it stops you from missing one or counting one twice.
A square has a perimeter of . If its side length is increased by , what will be the new perimeter?
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First find the original side: .
The new side is , so the new perimeter is .
Another way: every one of the four sides grows by , so the perimeter grows by cm, giving cm.
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Interactive Activity
Visualise how to calculate the perimeter of different polygons step by step
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Frequently asked questions
The questions students bump into most on this topic
The perimeter of a shape is the total length of its boundary, the distance all the way round its edge. To find it, add the lengths of every side. A triangle with sides of 5 cm, 4 cm and 3 cm has a perimeter of 5 + 4 + 3 = 12 cm. The order does not matter, as long as every side is counted once.
Add the lengths of all the sides. Two shortcuts save time: a rectangle has two equal lengths and two equal widths, so its perimeter is 2 × (length + width), and a square has four equal sides, so its perimeter is 4 × side. A square with 2 m sides has a perimeter of 4 × 2 = 8 m.
Add all four sides, or use the shortcut: a rectangle has two equal lengths and two equal widths, so its perimeter is 2 × (length + width). For a rectangle 5 cm long and 3 cm wide, that is 2 × (5 + 3) = 16 cm. Both ways give the same total.
Add the lengths of all three sides. An isosceles triangle has two equal sides, so its perimeter is 2 × the equal side + the base: equal sides of 5 cm and a base of 3 cm give 2 × 5 + 3 = 13 cm. An equilateral triangle has three equal sides, so its perimeter is 3 × side: 3 × 7 = 21 cm.
First work out any missing side from the sides you know: in the lesson’s L-shape the left edge is 3 + 2 = 5 cm and the top is 3 − 1 = 2 cm. Then add every side, going round in one direction so none is missed, which gives 16 cm. A quicker way: slide the edges out into a rectangle and use 2 × (5 + 3) = 16 cm.
Perimeter is the distance around the outside of a shape, like walking around the edge of a playground. Ask your child to add up the sides as they go: a triangle with sides 5, 4 and 3 cm is 5 + 4 + 3 = 12 cm. For a rectangle, two sides match two sides, so add two and double.
What's next?
Found this one hard? Go one step back first. Feeling confident? Carry on to the next lesson.
