Question

square x has an area of 100 square units. Square Y has a perimeter that is half of the perimeter of square x. What is the area of square y?

Answer 1

each side of x is 10 units since it is square
then each side of y must be 5 units
and its area is 25 square units

In fact the ratio of areas of any two similar figures is the square of the linear scale ratio between them.

Answer 2

Square X, s = side
Area, A = s^2
100 = s^2
Take square root of both sides
10 = s

Square X, s = side
Perimeter, P = 4s
s = 10
P = 4(10)
P = 40

Square Y, s = side
Perimeter of Sq. Y = 1/2 Sq. X
Perimeter of Sq X = 40,
P = 1/2 (40) = 20
P = 4s
20 = 4s
s = 5

Square Y, side = s
Area, A = s^2
s = 5
A = 5^2
A = 25 sq units