If you put 6 equilateral triangles together as shown below, you can make a regular hexagon. What is the area, in square units, of a regular hexagon of side lenght 6 units?

Question

anonymous · Answer

hlep me

anonymous · Answer

help me

anonymous · Answer

r u still there?

anonymous · Answer

attachment

anonymous · Answer

Find the area of each triangle and add them up

anonymous · Answer

I know what u mean, helps if y u post a pic.

anonymous · Answer

It's not my question estudier

anonymous · Answer

I wasn't talking to u...

anonymous · Answer

I was just making a suggestion

anonymous · Answer

Our posts are crossing....

anonymous · Answer

OK, as Heromiles says, you need to calculate the area of 1 triangle and multiply it by 6.

Can u do that?

anonymous · Answer

She would have to understand how to find the height of the equilateral triangle

anonymous · Answer

Equilateral means all the sides of the triangle are the same length. If you can find the area of one triangle, you can find the area of the entire hexagon by multiplying the area of one triangle by 6.

To find the area of a triangle, you need a base measurement (easy in this case; it is 6) and a height measurement. For equilateral triangles, the height measurement will be the measure of the midpoint of the base of the triangle to the top vertex/point.

You can figure out this height using Pythagorean theorem (a^2 = b^2 + c^2). Let me draw a picture, then I'll continue.

anonymous · Answer

root(3)
Area of an Equilateral triangle = ------- * (side)^2
                                                              4

Here side of the equilateral triangle will be 6 units

                                              root(3)                       root(3)
so Area of 1 Eqltrl trngl = -------- * (6)^2  = -------- * 36 = 9 root(3)
                                                   4                                   4

Since the regular hexagon is made up of such 6 equilateral triangles...
its area = 6* 9 root(3)     i.e.$$54\sqrt{3}$$

anonymous · Answer

So, once you've constructed the height, you will notice two right angle triangles.

The base measurement for each is 3 units (half the base of the equilateral triangle), and the hypotenuse is 6 cm. Using these numbers in the formula, you get.

6^2 = 3^2 + c^2
36 = 9 + c^2
c^2 = 36 - 9
c^2 = 27
c = sqrt(27)

You can now find the area of each triangle using the formula A = 1/2 * bh

anonymous · Answer

@MathDrills
why do we need to go through all this procedure....
we do not need to calculate the height.........
since length of side is known, we can use the formula I used...