Question

An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b.
Which statements about finding the area of the equilateral triangle are true? Select three options.

The apothem can be found using the Pythagorean theorem.
The apothem can be found using the tangent ratio.
The perimeter of the equilateral triangle is 15 cm.
The length of the apothem is approximately 2.5 cm.
The area of the equilateral triangle is approximately 65 cm2.

Answer 1

Correct choices:
- The apothem can be found using the Pythagorean theorem.
- The apothem can be found using the tangent ratio.
- The length of the apothem is approximately 2.5 cm.

Brief justifications:
- Using the right triangle formed by radius R = 5, half a side b = 8.7/2 = 4.35, and apothem a: a = sqrt(5^2 − 4.35^2) ≈ 2.47 (≈2.5).
- Using the 30°–60° right triangle (tan 30° = a/(s/2)): a = (8.7/2)·tan30° ≈ 2.51 (≈2.5).
- Perimeter = 3·8.7 = 26.1 cm, not 15 cm, so that statement is false.
- Area = (1/2)·base·height = (1/2)·8.7·(8.7·√3/2) ≈ 32.75 cm², not ≈65 cm².