Find the area of this shape

Question

Find the area.

Answer 1

Hi Isbella B.,

Since your figure doesn't transmit on the Wyzant platform, perhaps you could describe a bit more? Is height the distance from the center of the hexagon to an edge as a perpendicular to it, or is it something else?

If that's what you mean, you do a little trigonometry. That segment, and the one from the center of the hexagon to an adjacent vertex, and the (1/2) of a side joining them, make a 30-60-90 degree right triangle (with the 30 at the center), right? Always look for a 30-60-90 triangle possibility first! And you know how to do an area for it, ratio the sides up from the length of the side you know (and you know that the sides are in the ratio 1:2:(3)^0.5). And there are 12 of them comprising the entire hexagon area.

-- Cheers, -- Mr. d.

Answer 2

The hexagon can be divided into 6 equilateral triangles.

The height of such a triangle is the apothem of the hexagon, i.e. 1/2 the height of the hexagon..

The side of the equilateral triangle and therefore of the hexagon is 2...remember the relationship of the sides in a 30-60 rt triangle.

The area is (1/2) * apothem * perimeter.

With those hints you should be able to solve your problem.