A rectangle and a square have the same perimeter. What is the area of the square if the sides

A rectangle and a square have the same perimeter. What is the area of the square if the sides of the rectangle are 1.8 cm and 3.4 cm long?

The perimeter of a rectangle (Pпр) is equal to the sum of the lengths of all its sides. Taking into account the fact that in a rectangle the opposite sides are pairwise equal, we can write:

Ppr = a + b + a + b = 2a + 2b, where a is the length of the rectangle, b is its width.

Ppr = 2 * 3.4 + 2 * 1.8 = 6.8 + 3.6 = 10.4 cm.

The perimeter of the square is:

Pkv = a + a + a + a = 4a, where a is the length of the side of the square.

Knowing the perimeter of a square, you can calculate its side:

Pкв = Рпр = 10.4 cm,

a = Pkv / 4,

a = 10.4 / 4 = 2.6 cm.

Let’s calculate the area of the square:

Skv = a ^ 2 = 2.6 ^ 2 = 6.76 cm2.

Answer: 6.76 cm2.