What is the area of an equilateral triangle with sides of length 1 unit?

Question

Use the Pythagorean theorem to help you determine the are of an equilateral triangle with sides of length 1 unit. 

Answer 1

Draw and label of diagram.

Draw an altitude, "a," from the base to the opposite vertex.

The altitude bisects the base.

You two congruent right triangles withe legs of 0.5 and "a," and a hypotenuse of 1.

 

1² = (0.5)² + a²

1 = 0.25 + a²

0.75 = a²

3/4 = a²

√3 / 2 = a

 

Area of equilateral triangle is (0.5)(1)(√3 / 2), or √3 / 4.