which statements about finding the area of the equilateral triangle are true? select three options. the…

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.

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

Answer:

A. The apothem can be found using the Pythagorean theorem. B. The apothem can be found using the tangent ratio. E. The area of the equilateral triangle is approximately 65 cm².

Explanation:

Step1: Apothem - Pythagorean theorem

In an equilateral - triangle, if we consider half of a side and the side of the triangle, the apothem, half - side, and side of the triangle form a right - triangle. So, the apothem can be found using the Pythagorean theorem (a^{2}+b^{2}=c^{2}).

Step2: Apothem - tangent ratio

If we know the central angle of an equilateral triangle ((120^{\circ}), and half of it is (60^{\circ})) and half of the side length, we can use the tangent ratio (\tan\theta=\frac{\text{opposite}}{\text{adjacent}}) to find the apothem.

Step3: Area calculation

The area of a regular polygon is (A = \frac{1}{2}ap), where (a) is the apothem and (p) is the perimeter. First, find the apothem and perimeter. The side length of the equilateral triangle is (s = 10) cm (since half - side is 5 cm), so (p=3s = 30) cm. After finding the apothem (using Pythagorean or tangent), and substituting into the area formula, we can get an area close to (65) cm². The perimeter of the equilateral triangle with half - side 5 cm is (3\times10 = 30) cm, so the statement about the perimeter being 15 cm is false. And without proper calculation, we can't say the apothem is approximately 2.5 cm.