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21.7 cm2 32.5 cm2 112.5 cm2 65 cm2
Each interior angle measures 120 degrees. |dw:1370835520501:dw|
For each triangle, the two angles near the side of the haxagon are 60 degrees each, so the third angle is also 60 degrees. |dw:1370835651695:dw|
Now you need to find the area of an equilateral triangle whose sides measure 5 cm.
Are you following this?
The small triangle on the right has one leg measuring 2.5 cm and a hypotenuse measurung 5 cm. With the Pytagoras theorem, we can find h, the measure of the other leg, which is also the height of the large triangle.
I got 5.59 for the height.
The height can't be 5.59 because the hypotenuse is 5, and the height can't be larger than the hypotenuse.
Oh.. I put them in the wrong posistion. I did 2.5^2 + 5^2 = h^2
You need to add the squares of the legs to equal the square of the hypotenuse. That's why it's 2.5^2 + h^2 = 5^2
Now we see that for one triangle, we have a base of 5 cm and a height of sqrt(18.75) cm. The area of a triangle is A = (1/2)bh, where b = base, and h = height. Since the hexagon is made up of 6 congruent triangles, the area of the hexagon is 6 times the area of the triangle.
AH = area of the hexagon AH = 6(1/2)bh = 3bh AH = 3 * 5 cm * sqrt(18.75) cm AH = 65.0 cm^2
See, I didn't know that I had to break the Hexagon into 6 triangles... But thank you so much!
We break it up into simple shapes that we are familiar with, such as a triangle.