The area would be 441 m².
We first find the length of the given rectangle. We know area is length times width, that the area is 405 and the width is 15; this gives us:
405 = 15L
Divide both sides by 15:
405/15 = 15L/15
27 = L
Calculate the perimeter of the rectangle:
P = 2L + 2w = 2(27) + 2(15) = 84 m
The side of the square is 1/4 the perimeter of the rectangle we just found:
1/4(84) = 21 m
The area of a square is equal to its side length squared:
A = s² = 21² = 441 m²
