Question

the area of an equilateral triangle is 108 radical 3 ft^2. What is the length of a side and the apothem in simplest radical form?

Answer 1

So the apothem becomes: \[\text{ap}=\frac{\sqrt{3}}{6}l\] but we're not given \(l\).

Answer 2

Therefore \[\text{area of an eq. triangle} : A=\dfrac{\sqrt{3}}{4}a^2\]\[a=\sqrt{\frac{4A}{\sqrt{3}}}=\sqrt{\frac{4(108\sqrt{3})}{\sqrt{3}}}=\sqrt{4(108)} =\sqrt{432}\]\[a=r\]\[\text{side of an equil. triangle} : l=\sqrt{3}r\]\[\color{red}{\boxed{l=\sqrt{3}\cdot \sqrt{432} = \sqrt{3\cdot 432} = \sqrt{ 1296} =36}} \]

Answer 3

i need some help anyone plz?

Answer 4

The apothem for an equilateral triangle \[\text{ap}=\frac{\sqrt{3}}{6}l\]\[\color{red}{\text{ap}=\frac{\sqrt{3}}{6}\cdot 36 = \sqrt{3}\cdot 6 = 6\sqrt{3}}\]

Answer 5

so would the apothem for this problem just be 6 radical 3
and length would be 36 right?

Answer 6

but thank you, your steps really helped(:

Answer 7

Well, there really isnt a need to ask when it's been solved, haha. Just look at my posts to determine what the apothem (ap) and length would be.

Answer 8

And definitely do not forget your units.