1. ## One last problem.

I hope.
A square tablecloth lies flat on top of a circular table with are 3.14 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?

They got the answer as 2.

2. ## one last problem

Originally Posted by dnntau
I hope.
A square tablecloth lies flat on top of a circular table with are 3.14 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?

Hi dnntau,
Calculate the circle radius. What is the relationship of it to the side of the inscribed square.Square the derived lenght.
What "they said" is true

They got the answer as 2.

bjh

3. Right, it's 2 square feet.

The area of a circle is given by $\displaystyle \pi r^2$, and is given as 3.14

$\displaystyle \pi r^2 = 3.14$

Taking pi as 3.14, we get:

$\displaystyle r^2 = 1$

$\displaystyle r = 1 ft$

Now, the radius of the circle is from the centre to the edge of the circle. But the centre of the square table cloth to the corner is also equal to r, so, it is 1 ft.

Since you have 4 corners, you can take two adjacent corners and form a riht angled triangle with them.

From there, you can fing the hypotenuse, which happens to be the side of the square. Let's find that.

$\displaystyle s^2 = 1^2 + 1^2$

$\displaystyle s = \sqrt{2}$

Now the area of a square is given by length x length.

So, area of the table cloth = $\displaystyle \sqrt2 \times \sqrt 2 = 2 ft^2$

4. Thanks everyone.