Question

an equilateral triangle with center f is shown below.
what is the area of the triangle?
round your answer to the nearest tenth.

square inches

Explanation:

Step1: Find the side length of the equilateral triangle

For an equilateral triangle, if the distance from the center (centroid) \(F\) to a vertex is \(R = 9\) inches. The formula relating the side length \(a\) of an equilateral triangle and the distance from the center to a vertex (circum - radius) is \(R=\frac{a}{\sqrt{3}}\).
So, \(a = 9\sqrt{3}\) inches.

Step2: Calculate the area of the equilateral triangle

The area formula for an equilateral triangle is \(A=\frac{\sqrt{3}}{4}a^{2}\).
Substitute \(a = 9\sqrt{3}\) into the formula:

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Answer:

\(105.2\) square inches