Question

Shown below is an image of a circle and six equilateral triangles. The circumference of the circle is 18.85 cm. What is the area of ONE equilateral triangle in cm2? Assume √3 = 1.732 and π = 3.14.

Answer 1

Correct Answer: 5

To find the area of one equilateral triangle, we first deduce the radius of the circle using the circumference.

Step 1: Calculate the radius of the circle. 
 

The circumference \( C \) of a circle is given by \( C = 2\pi r \).
Given \( C = 18.85 \) cm and \( \pi = 3.14 \), we solve for \( r \):
\( 18.85 = 2 \times 3.14 \times r \)
\( r = \frac{18.85}{6.28} \approx 3 \) cm

Step 2: Determine the side length of the equilateral triangles.
 

Since the circle is circumscribed around six equilateral triangles, each triangle's vertex touches the circle. The side length \( s \) of the equilateral triangle is equal to the circle's radius \( r \). Thus, \( s = 3 \) cm.

Step 3: Calculate the area of one equilateral triangle.
 

The area \( A \) of an equilateral triangle with side length \( s \) is given by the formula:
\( A = \frac{\sqrt{3}}{4} \times s^2 \)
Substituting \( s = 3 \) cm and \( \sqrt{3} = 1.732 \):
\( A = \frac{1.732}{4} \times 9 = \frac{15.588}{4} \)
\( A \approx 3.897 \) cm²

Step 4: Verify the solution falls within the specified range.
 

The calculated area of one equilateral triangle is approximately 3.897 cm², which falls within the provided range of 5 ± 5.