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).
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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
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What is the perimeter of a square with side length ?
Correct! 🎉 +10 pointsNot quite right
The perimeter of a square is calculated as 4 × side length. For a side length of , the perimeter is .
Find the perimeter of a rectangle with length and width .
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The perimeter of a rectangle is calculated as 2 × (length + width). For a length of and a width of , the perimeter is .
The perimeter of an equilateral triangle is . What is the length of one side?
Correct! 🎉 +20 pointsNot quite right
For an equilateral triangle, all sides are equal. To find one side, divide the perimeter by 3: .
An isosceles triangle has a base of and two equal sides of each. What is its perimeter?
Correct! 🎉 +20 pointsNot quite right
The perimeter of a triangle is the sum of all its sides. Add .
An irregular hexagon has edges of the following lengths: , , , , , and . What is its perimeter?
Correct! 🎉 +20 pointsNot quite right
The perimeter of an irregular hexagon is the sum of its side lengths: .
A square has a perimeter of . If its side length is increased by , what will be the new perimeter?
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The side length of the square is . Increasing it by gives . The new perimeter is .
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Interactive Activity
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Students Also Ask
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Add all four sides, or use the formula. Because a rectangle has two equal lengths and two equal widths, its perimeter is 2 × (length + width). For a rectangle 5 cm by 3 cm, that gives 2 × (5 + 3) = 16 cm. Both methods reach the same total.
A square has four equal sides, so add one side four times, or multiply one side by 4. If each side is 2 m, the perimeter is 4 × 2 = 8 m. The shortcut works because every side is exactly the same length.
Add the lengths of all three sides. For an isosceles triangle with two equal sides a and base b, the perimeter is 2 × a + b. For an equilateral triangle with equal sides a, it is 3 × a. For example, sides of 5 cm, 5 cm and 3 cm give 13 cm.
First work out any missing side lengths from the edges you already know. Then add every side, going round the shape in one direction so none is missed. You can also rearrange the edges into a rectangle and use 2 × (length + width) to reach the same answer.
An L-shape fits inside a rectangle, and its edges can be slid across to line up with the rectangle's sides without changing their total length. The boundary therefore stays exactly as long. For the worked example, both methods give 16 cm.