√ 36 rational irrational real natural whole integer

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

Irina-Kira [14]

Answer:

Radius - 4

Apothem - 2

Area - $12\sqrt{3}$ 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...

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

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.

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

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

Happy April Fool's btw, lol.

4 0

3 years ago

On average, cody runs 4 miles in 38 minutes. How fast should he plan to run a 10-mile race if he maintains this place.

viva [34]

C. 1 hour and 35 minutes

6 0

3 years ago

Help please solve for X

Mila [183]

Answer:

Step-by-step explanation:

those angles are congruent because they are vertical angles

6x+4 = 58 ; subtract 4 from both sides

6x = 58-4 ; combine like terms

6x = 54; divide both sides by 6

x= 9

3 0

3 years ago

Read 2 more answers

What is the area of the polygon shown above? Show all your work. Please include the appropriate units in your answer.

sukhopar [10]

Answer:24 by 5

Step-by-step explanation:

6 0

3 years ago

Rafi had a board that was 15 1/2 feet long. He cut three pieces off the board that are each 3 7/8 feet long. How much of the boa

sattari [20]

Answer:

Step-by-step explanation:

To answer this question, first we need to figure out how much of the board Rafi cut off.

To do this, we need to multiply the length of each piece by the number of pieces he cut off.

3 7/8 = 3.875

3.875 * 3 = 11.625

Now, because we knew Rafi cut off 11.625 feet off of the board, we just need to subtract this length from the length of the entire board to find the remaining length.

15 1/2 = 15.5

15.5 - 11.625 = 3.875

There is 3.875 feet or 3 7/8 of the board left.

7 0

2 years ago

√ ​36 rational irrational real natural whole integer

√ 36 rational irrational real natural whole integer