Question

What is the area of the equilateral triangle with sides 10?

Answer 1

Hint: Area of equilateral triangle is the amount of space it takes in 2-d. It is the special type of triangle in which all the sides are equal. Also, the equilateral triangle measure of all sides of the triangle is 60. We can find the area of a triangle if any one side of the triangle is known since all other remaining sides are also equal.

Complete step-by-step solution:
We know that the area of the equilateral triangle is given by, Area= $\dfrac{\sqrt{3}}{4}{{a}^{2}}$ where a is the side of the triangle. It is a regular polygon with three sides.
So, we can draw the diagram as shown below.

It is a special case of the isosceles triangle where the third side is also equal. In an equilateral triangle ABC, AB=BC=CA. In equilateral triangles the centroid and orthocenter are at the same points. A triangle is equilateral if and only if the circumcenter of any three of the smaller triangles have the same distance from the centroid. In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle.
Now, in the given question we are given the side of the equilateral triangle as 10.
Now, substituting the value in the formula ,Area=$\dfrac{\sqrt{3}}{4}{{a}^{2}}$
We get,
$\begin{align}
  & Area=\dfrac{\sqrt{3}}{4}{{10}^{2}} \\
 & \Rightarrow \dfrac{\sqrt{3}}{4}\times 100 \\
 & \Rightarrow \sqrt{3}\times 25 \\
 & \Rightarrow 25\sqrt{3} \\
\end{align}$
So, after substituting the values we get the area as above.

Note: Make sure we don’t get confused in the properties of triangles. Apart from that we do not need to use much of the properties here. It seems to be a direct question where we can just apply the concept of equilateral triangle and the very basic concept of it.