L5 · Finding an unknown side length from a perimeter

Learning goal

“I can find a missing side of a polygon when I know the perimeter and the other sides - by taking the known sides away from the perimeter.”

Unknown — a value we do not know yet and must find. We write it as a blank: □.

Perimeter — (from L4) the sum of all the side lengths of a polygon.

Subtraction — taking away. If the perimeter is the whole sum, taking away the known sides leaves the unknown side.

Worked example

A triangle has a perimeter of 21 cm. Two sides are 8 cm and 7 cm. Find the third side. Step 1: The perimeter is all three sides added: 8 + 7 + □ = 21. Step 2: Add the known sides first: 8 + 7 = 15. Step 3: Take them away from the perimeter: 21 - 15 = 6 cm. Check: 8 + 7 + 6 = 21. Say it plainly: the perimeter is the whole. Take away the parts you know, and the part left is the unknown side.

Check yourself — explain it

We subtract the known sides from the perimeter because...

Paired problem — example still visible

A four-sided polygon has perimeter 25 cm. Three sides are 6 cm, 7 cm, and 5 cm. Find the fourth side. -> 7 cm (25 - 18 = 7; check 6 + 7 + 5 + 7 = 25)

Faded completion — last step is yours

"A triangle has perimeter 19 cm and known sides 9 cm and 6 cm: unknown side = 19 - (9 + ___) = ___ cm" -> 6; 4

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz