# Question Video: Calculating the Perimeter of Figures Formed by Squares and Rectangles by Writing an Algebraic Expression Mathematics

Express the perimeter of the figure below in terms of π₯.

01:45

### Video Transcript

Express the perimeter of the figure below in terms of π₯.

So what is a perimeter? A perimeter is a distance around a shape. So letβs go ahead and highlight some of the lengths that we are ready know. Here we have 16π₯, 16π₯, π₯, and 15π₯. So in order to find the perimeter, we need to find the remaining side lengths. Letβs begin with this one.

It is the exact same length as these two yellow lengths, put together. So this entire side will be 16π₯ plus π₯. And combining like terms, we get 17π₯. So we can label the missing side 17π₯. Now this last missing piece create an entire side with the 15π₯. So this side will be represented by 15π₯ plus question mark. So weβre excluding this yellow piece. It is just the pieces that are parallel the question mark and the 15π₯.

So that 15π₯ plus question mark will be the same length as the 16π₯. So we can set it equal to 16π₯. So 15π₯ plus question mark equals 16π₯. So letβs subtract 15π₯ from both sides. So question mark is equal to π₯ or one π₯. So this length is π₯.

So now we have every single side length. So now, we can find the perimeter by adding them all together. So we have 16π₯ plus 16π₯ plus π₯ plus π₯ plus 15π₯ plus 17π₯. And adding these all together will give us the perimeter. And we get 66π₯. Therefore, our final answer in terms of π₯ will be 66π₯ length units.