The area of the rectangle is 360.64 cm2 and its width is 8.4 cm. find the area of a square if its perimeter

The area of the rectangle is 360.64 cm2 and its width is 8.4 cm. find the area of a square if its perimeter is equal to the perimeter of the rectangle.

1. Let’s write down the formula for the area of a rectangle:
S = a * b;
2. Let us find from here the length of this rectangle:
b = S / a = 360.64 / 8.4 ~ 43 (cm);
3. Now let’s find the perimeter of this rectangle:
P = 2 * (a + b);
P = 2 * (8.4 + 43) = 102.8 (cm);
4. Find the side of the square:
P = 4 * a;
a = 102.8 / 4 = 25.7 (cm);
5. Find the area of the square:
S = a ^ 2;
S = 27.7 * 25.7 = 660.49 ~ 660.5 (cm2);
Answer: the area of the square is 660.5 cm2.