To find: The function that models area of equilateral triangle in terms of its length x of one of its sides.
The function that models area of given equilateral triangle is .
Draw the figure of equilateral triangle as shown below.
Area of triangle is,
The length of side of equilateral triangle is .
In Figure (1) is median, it bisects so is .
Use Pythagorean theorem in triangle shown in Figure (1).
Substitute x for , for in above equation.
Subtract from both sides of above equation.
Take square root of above equation and switch sides.
Summarize the all the information as shown in table below.
|In Words||In Algebra|
Use the information in the table and model the function.
Thus, the function that models area of equilateral triangle is .
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