Quadrilaterals, tiling and the eight directions · Usually met around P4
The rhombus
Four equal sides; perimeter = side × 4.
How to do it
Method
Four equal sides; perimeter = side × 4
5 × 4 = 20
Another way
Add the sides
5 + 5 + 5 + 5 = 20
In full
A rhombus is a four-sided shape with all four sides the same length. Both pairs of opposite sides are parallel, so a rhombus is a parallelogram too, and its opposite angles are equal. Its angles needn't be right angles: a rhombus with four right angles is a square. The perimeter is the distance all the way round, all the sides added up; with four equal sides, a rhombus's perimeter = side × 4, and side = perimeter ÷ 4. To draw one, draw a side, then the other three the same length; or join four equal sticks end to end. Or check the perimeter by adding the four sides.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
One side of a rhombus is 20 cm. What is its perimeter in cm?
Show the answer and working
Answer: 80 cm
A rhombus has four equal sides: 20 × 4 = 80.
Example 2
A rhombus has a perimeter of 112 cm. How long is each side, in cm?
Show the answer and working
Answer: 28 cm
The four sides are equal: 112 ÷ 4 = 28.
Example 3
Four straws each 14 cm long are joined end to end into a four-sided shape. What shape must it be?
- A. A square
- B. A trapezium
- C. A rectangle
- D. A rhombus
Choose the right answer
Show the answer and working
Answer: D. A rhombus
A four-sided shape with four equal sides is a rhombus (a square is one kind).
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