Respuesta :

so hmm check the picture below

using the 30-60-90 rule, we get that much.. .bear in mind, an equilateral triangle has all equal sides, and therefore, all equal angles, so each angle is 60°, run a median through it from the center, and you split it in half

[tex]\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \begin{cases} s=\textit{length of one side}\\ ----------\\ s=14\sqrt{3} \end{cases}\implies A=\cfrac{(14\sqrt{3})^2\sqrt{3}}{4} \\\\\\ A=\cfrac{14^2\cdot 3\sqrt{3}}{4}\implies A=\cfrac{588\sqrt{3}}{4}\implies A=147\sqrt{3}[/tex]
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onyebuchinnaji

The area of an equilateral triangle with apothem 7 cm is determined as 254.52 cm².

What is the area of an equilateral triangle?

The area of an equilateral triangle with apothem 7 cm is calculated as follows;

A = ¹/₂aP

where;

  • a is the apothem
  • P is the perimeter of the triangle

Half length of a side the triangle

  • let the half of a side = x
  • an apothem is a vertical height from a side to the middle of the triangle

tan 30 = a/x

x = a/tan 30

x = 7/tan 30

x = 12.12 cm

complete length of a side = 2(12.12 cm) = 24.24 cm

P = Perimeter = 3 x 24.24 = 72.72 cm

A = ¹/₂aP

A = ¹/₂(7)(72.72)

A = 254.52 cm²

Learn more about apothem here: https://brainly.com/question/10580427

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