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uranmaximum [27]
3 years ago
14

The perimeter of an equilateral triangle is 12\/3 cm. Find the radius, apothem and area of the equilateral triangle.

Mathematics
1 answer:
Irina-Kira [14]3 years ago
4 0

Answer:

<u><em>Radius -  </em></u>4

<u><em>Apothem -  </em></u>2

<u><em>Area - </em></u>12\sqrt{3} or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

~~~~

This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

12\sqrt{3}  \div3 = 4\sqrt{3}

Now that we know the side lengths, we can get this started!

~~~~

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.

Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6

By the way, the formula for the area can be either of the two:

A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS

we can easily find the area using the first formula.

A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}

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>

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