AA circle has a diameter of 12 units find the area

36π units² or 113.04 units²

Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle which is Area = πr².

Notice that here, we're given the diameter instead of the radius. It's important to understand that the radius is equal to half of the diameter so the radius of this circle will be equal to half of 12 units or 6 units.

So plugging into the formula, we have (π)(6 units)².

A common mistake is to plug 12 units into the formula but remember that we must plug in the radius and not the diameter.

Multiplying, (6 units)² is equal to 6 units · 6 units or 36 units².

So we have 36π units².

So the area of the circle is 36π units².

Now, remember that π is approximately equal to 22/7 or 3.14 so we can estimate the area of the circle by plugging in 3.14 for π.

So we have (36)(3.14) which is equal to 113.04 units².

So the area of the circle is approximately equal to 113.04 units².

∠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.