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

The Perimeter Of An Equilateral Triangle Is 123 Cm Find The Radius Apothem And Area Of The Equilateral Triangle class=

Sagot :

Sweeteany34

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.

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