# Question Video: Calculating the Areas of Two Squares given the Sum of Their Perimeters and the Side Length of One of Them Mathematics • 6th Grade

If the sum of the perimeters of two squares is 112 cm and the side length of one of them is 9 cm, find the sum of their areas.

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### Video Transcript

If the sum of the perimeters of two squares is 112 centimeters and the side length of one of them is nine centimeters, find the sum of their areas.

In this question, we’re given some information about two different squares. Let’s call them 𝐴 and 𝐵. We’re told that the side length of one of these squares is nine centimeters. We’ll assign these lengths to square 𝐵. Now, we’re actually told that the sum of the perimeters of our two squares is 112 centimeters. And we’re looking to calculate the areas.

Now, the formula that we use to calculate the area of a square is side length squared. So we can quite easily calculate the area of square 𝐵. But we can’t calculate the area of square 𝐴 without knowing its side length. So we’re going to begin by calculating the perimeter of square 𝐵 and subtracting this from the total perimeter. Now, the perimeter is the total distance around the square. So the perimeter of square 𝐵 must be nine multiplied by four, since it has four equal sides. Nine times four is 36. So we find the perimeter of square 𝐵 is 36 centimeters.

We know that the sum of the perimeters of our squares is 112 centimeters. So if we subtract 36 from 112, that gives us the perimeter of square 𝐴. That’s 76 centimeters. We said that to calculate the area of square 𝐴, we need to find its side length. Now, remember, when we knew the side length, we calculated the perimeter by multiplying this by four. This time, we know the perimeter and we’re looking to find the side length. So we’re going to divide 76 by four. That’s 19. And so we’ve found that the side length of square 𝐴 is 19 centimeters.

We’re now ready to find the area of each of our squares. The area of square 𝐴 is 19 times 19 or 19 squared. That’s 361. And since we’re working in centimeters, it’s 361 centimeters squared. The area of square 𝐵 is nine squared. That’s 81 square centimeters. The question wants us to find the sum of the areas of our squares. So that’s the sum of 361 and 81, which is 442 or 442 square centimeters.