Question

a side of an equilateral triangle is 20 cm long. what is the area of the triangle? do not round any intermediate computations, and round your answer to the nearest tenth.

Explanation:

Step1: Find the height of the equilateral triangle

Use the Pythagorean theorem. The base of the right - triangle formed by the height is $\frac{20}{2}=10$ cm. Let the side of the equilateral triangle be $a = 20$ cm and the height be $h$. Then $h=\sqrt{20^{2}-10^{2}}=\sqrt{400 - 100}=\sqrt{300}=10\sqrt{3}$ cm.

Step2: Calculate the area of the equilateral triangle

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base is 20 cm and the height is $10\sqrt{3}$ cm. So $A=\frac{1}{2}\times20\times10\sqrt{3}=100\sqrt{3}\approx173.2$ $cm^{2}$.

Answer:

$173.2$