# Video: AQA GCSE Mathematics Higher Tier Pack 1 β’ Paper 2 β’ Question 21

AQA GCSE Mathematics Higher Tier Pack 1 β’ Paper 2 β’ Question 21

01:50

### Video Transcript

A trapezium is shown below. The length of side π§ is six times the length of side π€. The area of the trapezium is 409.5 square centimeters. Calculate length π§.

So first, we know that itβs a trapezium. And the length of side π§ is six times the length of side π€. So we could say that π§ is equal to six π€. Weβre also told the area of the trapezium.

The area of a trapezium is one-half times π plus π times the height, where π and π are the bases and in this case, π€ and π§, π and π. And we know what the area actually is: 409.5 square centimeters.

We replace π΄ with 409.5, π and π with π€ and π§, and the height of the trapezium is 18. Since weβre trying to find the length of π§, we either need to solve for π§ with our equation or solve for π€.

And then, once we know π€, substitute it in here, and take that number times six. And that will be the length of π§. So letβs go ahead and replace π§ with six π€ and now simplify.

π€ plus six π€ is seven π€. We can also take one-half times 18, which gives us nine. And if we take nine times seven π€ on the right-hand side of the equation, we get 409.5 is equal to 63π€.

Dividing both sides by 63, we find that π€ is equal to 6.5. And weβre to find the length of π§. And since π§ is equal to six π€, we need to take six times six and a half, resulting in 39.

Therefore, the length of π§ will be 39 centimeters.