Respuesta :

calculista

we know that

An equilateral triangle is a regular polygon, because all sides are equal

In a regular polygon the area is equal to

[tex]A=\frac{1}{2}*apothem*perimeter[/tex]

in this problem we have

[tex]apothem=2.16\ cm\\ perimeter=22.45\ cm[/tex]

substitute in the formula

[tex]A=\frac{1}{2}*2.16*22.45[/tex]

[tex]A=24.2\ cm^{2}[/tex]

therefore

the answer is

the area of the triangle is [tex]24.2\ cm^{2}[/tex]

Lanuel

The area of an equilateral triangle rounded to the nearest tenth is 24.2 [tex]cm^2[/tex].

Given the following data:

  • Apothem of triangle = 2.16 cm.
  • Perimeter of triangle = 22.45 cm.

What is an equilateral triangle?

An equilateral triangle can be defined as a type of triangle or regular polygon that has equal length of sides.

Mathematically, the area of an equilateral triangle is given by this formula:

[tex]Area = \frac{1}{2} \times apothem \times perimeter[/tex]

Substituting the given parameters into the formula, we have;

[tex]Area = \frac{1}{2} \times 2.16 \times 22.45\\\\Area = \frac{1}{2} \times 48.492[/tex]

Area = 24.246 ≈ 24.2 [tex]cm^2[/tex].

Read more on equilateral triangle here: https://brainly.com/question/11844452