Let's start by finding the area A_T of the triangle. Notice that all the sides of the triangle are congruent, so the triangle is equilateral. This means that every angle in the triangle has a measure of 60^(∘).
As we can see, by drawing the height of the triangle we create a 30^(∘)-60^(∘)-90^(∘) triangle. In a 30^(∘)-60^(∘)-90^(∘) triangle, the longer leg is sqrt(3) times the length of the shorter leg.
h = sqrt(3) * 3sqrt(3) ⇔ h = 9
Let's calculate the area A_T of the triangle.
The area of the triangle is approximately 46.77 square centimeters.
Finding the Area of the Circle
Now we will calculate the area A_C of the circle. Let's take a closer look at the circle.
We can see from the diagram that the length of the diameter of our circle is 12 centimeters. We know that the diameter is twice the length r of the radius.
12 = 2 r ⇔ r = 6
Knowing that the radius of our circle is 6 centimeters, we can calculate its area.
