Final answer:
The area of an equilateral triangle with side length a is given by the formula (\(\sqrt{3}/4\)) \(a^2\), so the correct answer is (c) \(\sqrt{3}/4\) \(a^2\).
Step-by-step explanation:
The question is asking for the area of an equilateral triangle with side length a. The area of an equilateral triangle can be found using the formula:
Area = (\(\sqrt{3}/4\)) \(a^2\)
Therefore, the correct answer is (c) \(\sqrt{3}/4\) \(a^2\). To understand why this formula works, consider that equilateral triangles can be split into two 30-60-90 right triangles. Using the properties of these right triangles, given that each side of the equilateral triangle is a, the height (h) can be found using the formula:
h = a \(\sqrt{3}/2\)
Once we have the height, we can then apply the generic formula for the area of a triangle, which is:
Area = 1/2 \(\times\) base \(\times\) height
Substituting the expressions for base and height of the equilateral triangle:
Area = 1/2 \(\times\) a \(\times\) \(a \sqrt{3}/2\) = \(\sqrt{3}/4\) \(a^2\), which is the area of the equilateral triangle.