Question

the triangle shown is an equilateral triangle. what is the area of the equilateral triangle with the length of each side equal to a? 1/2 asin(60°) 3asin(60°) 1/2 a²sin(60°) a²sin(60°)

Explanation:

Step1: Recall triangle - area formula

The area formula of a triangle is $A=\frac{1}{2}ab\sin C$, where $a$ and $b$ are two - side lengths of the triangle and $C$ is the included angle between them.

Step2: Identify values for equilateral triangle

In an equilateral triangle with side - length $a$, we can take $a = b=a$ and the included angle $C = 60^{\circ}$.

Step3: Substitute values into the formula

Substitute $a$ for $a$, $a$ for $b$, and $60^{\circ}$ for $C$ into the area formula $A=\frac{1}{2}ab\sin C$. We get $A=\frac{1}{2}a\times a\times\sin(60^{\circ})=\frac{1}{2}a^{2}\sin(60^{\circ})$.

Answer:

$\frac{1}{2}a^{2}\sin(60^{\circ})$