205k views
2 votes
A square tablecloth lies flat on top of a circular table whose area is π square feet. If the four corners of the tablecloth just touch the edge of the circular table, what is the area of the tablecloth, in square feet?

1 Answer

2 votes

The area of the tablecloth is 4 square feet.

Since the square tablecloth covers the circular table with its corners touching the edge, the side length of the square tablecloth (s) corresponds to the diameter of the circular table.

We know the table area is π square feet.

We can also express it in terms of the diameter using the formula for the area of a circle;

π = π × (s/2)²

Solve for side length:

Simplifying the equation, we get ;

s² = 4.

Therefore, the side length of the tablecloth is s = 2 feet.

The area of the tablecloth is simply the square of the side length: tablecloth area = s² = 4 square feet.

User Anam Ansari
by
8.2k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.