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zimovet [89]
2 years ago
6

Could someone please explain how to solve for the area?

Mathematics
2 answers:
mixas84 [53]2 years ago
8 0

9514 1404 393

Answer:

  779.4 square units

Step-by-step explanation:

You seem to have several problems of this type, so we'll derive a formula for the area of an n-gon of radius r.

One central triangle will have a central angle of α = 360°/n. For example, a hexagon has a central angle of α = 360°/6 = 60°. The area of that central triangle is given by the formula ...

  A = (1/2)r²sin(α)

Since there are n such triangles, the area of the n-gon is ...

  A = (n/2)r²sin(360°/n)

__

For a hexagon (n=6) with radius 10√3, the area is ...

  A = (6/2)(10√3)²sin(360°/6) = 450√3 ≈ 779.4 . . . . square units

IRINA_888 [86]2 years ago
6 0

Given

=> An Equilateral Hexagon with s = 10√3

To Find

=>The area of the Figure

Step-by-step explanation:

The area of an Equilateral Hexagon = 3√3s²/2

Inserting the value of <em>S</em>

<em>=</em><em>></em><em> </em><em>3</em><em>√</em><em>3</em><em>*</em><em>(</em><em>1</em><em>0</em><em>√</em><em>3</em><em>)</em><em>²</em><em>/</em><em>2</em>

<em>=</em><em>></em><em> </em><em>3</em><em>√</em><em>3</em><em>*</em><em>3</em><em>0</em><em>0</em><em>/</em><em>2</em>

<em>=</em><em>></em><em>3</em><em>√</em><em>3</em><em>*</em><em>1</em><em>5</em><em>0</em>

<em>=</em><em>></em><em>4</em><em>5</em><em>0</em><em>√</em><em>3</em>

<em>=</em><em>></em><em>7</em><em>7</em><em>9</em><em>.</em><em>4</em><em>4</em><em>2</em><em>8</em>

<h2><em>=</em><em>></em><em> </em><em>7</em><em>7</em><em>9</em><em>.</em><em>4</em><em>4</em><em> </em><em>squared</em><em> </em><em>units</em></h2>
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