Video: Writing Algebraic Expressions That Represent the Area and Perimeter of a Square

Bethani Gasparine

Write an expression for the area and perimeter of a square of side length 4𝑥 cm.

01:21

Video Transcript

Write an expression for the area and perimeter of a square of side length four 𝑥 centimeters.

Here, we have a square with side length four 𝑥 centimeters. But in a square, all side lengths are equal. And all angles are 90 degrees. So we can go ahead and label all of the sides as four 𝑥 centimeters. And even though we don’t need the angles for this question, each angle is 90 degrees. And it’s not a bad idea to fill that in.

So we want to write an expression for area and perimeter. If we let 𝑠 represent a side length, the area would be the side length squared because the area of a square would be length times width. But the length and the width are equal. That’s why we just call it the sides.

And then, the perimeter would be adding up all of the sides together. And there’re four of them. So we would take four times the side length, four 𝑠. So for the area, we’d need to square four 𝑥 centimeters, resulting in 16𝑥 squared centimeters squared. And for perimeter, we take four times four 𝑥 centimeters, resulting in 16𝑥 centimeters.

Therefore, the expression for area would be 16𝑥 squared centimeters squared. And the expression for perimeter would be 16𝑥 centimeters.

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