Answer:
<u><em>Radius - </em></u>4
<u><em>Apothem - </em></u>2
<u><em>Area - </em></u> 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...
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.
By the way, the formula for the area can be either of the two:
we can easily find the area using the first formula.
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
<em>Happy April Fool's btw, lol.</em>