Question

An equilateral triangle is inscribed in a circle with diameter 11 cm . How many square centimeters are in the area of the triangle? Express your answer as a decimal to the nearest tenth.

Answer 1

What have you attempted so far?

Answer 2

Nothing this is from a diagnostic worksheet that I already turned into my teacher. I didn't know what the answer was so I left it blank.

Answer 3

I see, well you should have at least guessed at the answer choices if there were any.

Let R be the radius of the circle. Let \(R\) be the radius of the circle. It is easy to see that the height of this triangle is \(\dfrac{(3 R)}{2}\) and the side is \(R \times sqr[t]\).

Do you follow so far?

Answer 4

Yes! I do actually.
I can get the area from that, thanks!

Answer 5

You are welcome.

Full work if anyone is interested:
$$(\dfrac{1}{2}) \times \dfrac{(3 R)}{2} \times R \times sqr[t] = (\dfrac{3}{4}) \sqrt{[3]} \times R^2$$

$$R = Diameter \div 2 = \dfrac{11}{2}$$
\(\textbf{Hence the answer is:}\)
$$(\dfrac{3}{4}) \times \sqrt{[3]} \times (\dfrac{11^2}{4}) = (\dfrac{3}{16}) \times \sqrt{[3]} \times 11^2 = 39.3$$
Note: Answer was rounded to the nearest tenth.