Answer:
Radius - 4
Apothem - 2
Area - [tex]12\sqrt{3}[/tex] or 20.8
Step-by-step explanation:
Try to draw out my explanation so you know what this looks like.
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This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...
[tex]12\sqrt{3} \div3 = 4\sqrt{3}[/tex]
Now that we know the side lengths, we can get this started!
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Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.
4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.
[tex]Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6[/tex]
By the way, the formula for the area can be either of the two:
[tex]A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS[/tex]
we can easily find the area using the first formula.
[tex]A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}[/tex]
The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...
So we can divide the big triangle into a mini triangle at the bottom left/right
The height (small leg) of that triangle would be the apothem
The hypotenuse of that triangle would be the radius.
I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius
Happy April Fool's btw, lol.
