Question

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

Answer: A B D

Explanation:

edge

Answer 2

options: 1,2 and 4

Explanation:

1) In a circle, the apothem is the perpendicular line segment that connects the Center to one chord's midpoint.

So we can calculate it by the Pythagorean Theorem:

`5^(2)=((8.7)/(2))^(2)+c^(2)\Rightarrow 25=18.92+c^(2)\Rightarrow c^(2)=25-18.9225\Rightarrow c=√(6.0775) \:c\approx2.5`

2) True The equilateral angle has 3 angles of 60º. And the line segment OC bisects the 60º so it is possible to calculate the apothem by the following relation, the tangent ratio:

`tan(30)=\frac{\overline{OC}}{\overline{OM}}=(apothem)/(adjacent\:leg)=(a)/(4.35)\Rightarrow (√(3))/(3)=(a)/(4.35)\:a\approx2.5`

3) False.

`2p =8.7+8.7+8.7\Rightarrow2p=26.1 cm`

4) True. Check number 1

5) False

`S=(l^(2)√(3))/(4)\approx 32.78`