Chapter 6.3, Problem 56E

To determine

To calculate: The area of an equilateral triangle such that length of its sides is 10.

Answer to Problem 56E

The area of triangle is $43.3\text{ sq units}$ .

Explanation of Solution

Given information:

An equilateral triangle such that length of its sides is 10.

Formula used:

The area of a triangle is denoted by $A=\frac{1}{2}ab\sin \theta$ where a andb are the length of its sides and $\theta$ is the included angle.

Calculation:

Consider the equilateral triangle such that length of its sides is 10.

An equilateral triangle has all sides of equal length and each angle is $60°$ .

Therefore, for area of equilateral triangle two side length are 10 each and included angle is $60°$ .

Recall that the area of a triangle is denoted by $A=\frac{1}{2}ab\sin \theta$ where a andb are the length of its sides and $\theta$ is the included angle.

Apply it,

  $\begin{array}{c}A=\frac{1}{2}\left(10\right)\left(10\right)\sin 60°\\ =50\left(\sin 60°\right)\\ =50\left(\frac{\sqrt{3}}{2}\right)\\ =43.3\end{array}$

Thus, the area of triangle is $43.3\text{ sq units}$ .