Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch apothem A = sq. in.
please answer in square root form.

Area of equilateral triangle is .

Step-by-step explanation:

We have, 6 inch  apothem means height = 6 inch but we also know that height of an equilateral triangle is .

∴

⇒  

⇒

Now, Area of equilateral triangle is  = , putting value of a we get:

⇒

⇒

⇒

∴Area of equilateral triangle is .

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.