Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal. What is the sum of the areas of the four triangles that will be removed from the rectangle?
So it’ll look like this:
It’s helpful just to know that a regular hexagon’s interior angles all measure 120°, but you can also calculate that using :
That means that the four triangles you’re cutting off the rectangle are each 30°-60°-90° triangles with 4-inch hypotenuses.
Those will have legs of 2 and , and therefore areas of . Since there are four such rectangles, the total area you’re cutting off is