A round table with a diameter of 180 cm and a height of 80 cm is covered with a square tablecloth

A round table with a diameter of 180 cm and a height of 80 cm is covered with a square tablecloth so that all four corners of the tablecloth touch the floor. What is the area of the tablecloth in square meters?

Let’s find the length of the diagonal of a square tablecloth, based on the fact that 180 cm of it goes along the diameter of the round table, and two ends hanging down to the floor account for 80 cm each.

d = 180 + 80 + 80 = 340 cm.

Let us express the length of the diagonal of the square in meters.

340 cm = 3.4 m.

The area of a square with side a is a ^ 2.

According to the Pythagorean theorem, the square of the hypotenuse (the diagonal of the square) is equal to the sum of the squares of the legs (sides of the square).

So a ^ 2 + a ^ 2 = d ^ 2.

2a ^ 2 = d ^ 2.

S = a ^ 2 = 1/2 * d ^ 2.

S = 1/2 * (3.4 * 3.4) = 11.56: 2 = 5.78 m2.

Answer: the area of the tablecloth is 5.78 m2.