SOLUTION: find the area of an equilateral triangle with an apothem having a length of 4 feet. round to the nearest tenth
Algebra ->
Triangles
-> SOLUTION: find the area of an equilateral triangle with an apothem having a length of 4 feet. round to the nearest tenth
Log On
The apothem of an equilateral triangle forms a 30-60-90 right triangle where the apothem is the long leg, one side of the triangle is the hypotenuse, and one-half of the side is the short leg.
With a tip o'the hat to Mr. Pythagoras, letting represent the measure of the hypotenuse, we can say:
And a little algebra and rationalizing the denominator gets us to:
Hence the measure of the short side of the triangle is:
The 30-60-90 triangle is one-half of the equilateral triangle, so:
