The floor of a theater was built in the shape of a hexagon. The interior angles of the hexagon are the same and one side is 10 meters long. How long is the perimeter of the floor in feet?

What is the area of the floor in square yards?

The perimeter is 196.85 feet. The area is 310.73 square yards

Since the problem states that the interior angles are the same, that tells of that the floor is a regular hexagon. So let's first calculate the perimeter. One side is 10 meters long. A hexagon has 6 sides, so the total perimeter is 10 * 6 = 60 meters. But we want the distance in feet, so we need to convert from meters to feet. You do this by multiplying by 3.28084, giving60 * 3.28084 = 196.85 feet

Now for the area. Since the floor is a regular hexagon, you can consider it to be comprised of 6 equilateral triangles, each side of which is 10 meters. You can also consider each triangle to be made up of two right triangles where the hypotenuse is 10 meters and one of the legs is 5 meters. Using the pythagoras theorem, the other leg of the triangle will be 5*sqrt (3) meters long (approximately 8.66 meters). Finally, the area of a triangle is 1/2 base times height. The base of each of those equilateral triangles will be 1/2 * 10 * 5 * sqrt (3). Since there are 6 of them, you get0.5 * 10 * 5 * sqrt (3) * 6 = 150 * sqrt (3) = 259.8076 square meters.

But we want square yards instead of square meters. So we convert by multiplying by 1.19599 giving259.8076 * 1.19599 = 310.73 square yards