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jasminesilva2907
.we can call segment "a" the radius, and if we do that, we calculate the area of the triangle as follows:
Look at the vertical line bisecting the triangle, made up of segments of length "a" and "h"
Now look at the smaller, right triangle towards the bottom left of the equilateral triangle, with sides "a", "h", and "S/2".
If we're taking "a" to be the radius (in our case 6 inches), then
h
a
=
sin
30
degrees, so
h
6
=
0.5
, so h = 3 inches. Therefore the height of the equilateral triangle is
6
+
3
=
9
inches.
The original equilateral triangle in the figure is bisected by the vertical line, making 2 right triangles of height 9 inches and a base of length S/2.
S
2
a
=
cos
30
, so
S
2
=
0.866
⋅
6
=
5.196
inches (rounding).
So, the original equilateral triangle in the figure is twice the area of this larger right triangle. A right triangle's area is
1
2
b
⋅
h
. We have TWO of them, so the total area is
2
⋅
1
2
b
⋅
h
=
5.196
⋅
9

...which works out to:
46.77 square inches (rounding)
GOOD LUCK
Ver imagen jasminesilva2907

The area of equiangular triangle with radius 6 inches is 27√3 square inches.

What is equiangular triangle?

A triangle with three equal interior angles is called equiangular triangle.

In an equiangular triangle, the measure of each of its interior angle is 60 degrees. Since, all the angles are equal therefore all the side will also be equal.

What is the formula for finding the area of equiangular triangle?

The formula for finding the area of equiangular triangle is

[tex]Area = \frac{\sqrt{3} }{4} a^{2}[/tex]

Where,

a is the side length of the triangle.

Let the side length of the equiangular triangle be a.

According to the given question.

We have a equiangular triangle with a radius 6.

Since, the radius of the equilateral triangle or equiangular triangle is given by

Radius = [tex]\frac{a}{\sqrt{3} }[/tex]

⇒ a = 6√3 inches.

Therefore, the area of equiangualr triangle is given by

[tex]Area = \frac{\sqrt{3} }{4} (6\sqrt{3} )^{2}[/tex]

⇒ [tex]Area = \frac{\sqrt{3} }{4} \times 36 \times 3[/tex]

[tex]\implies Area = 27\sqrt{3}[/tex]  square inches

Hence, the area of equiangular triangle with radius 6 inches is 27√3 square inches.

Find out more information about area of equaingular triangle here:

https://brainly.com/question/2272529

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