Answer:
(3 S.F)
Step-by-step explanation:
Diameter of circle (D) = one side of the equilateral ∆
Circumference of the circle = πD = 48 cm
Thus:
πD = 48
Divide both sides by π
D =
= 15.3 cm (approximated to nearest tenth)
Since all sides an equilateral ∆ are equal, therefore, and the diameter, D, of the circle given is the same as the length of one side of the ∆, therefore, all sides of the equilateral triangle would be 15.3 cm.
Recall that the area of a triangle can be found if we know lengths of the two sides of the ∆ and the measure of the included angle between both sides.
Since an equilateral ∆ has equal angles, each measuring 60°, then we already have all the information needed to calculate the area of the ∆.
Thus:
Length of the two sides = 15.3 cm and
15.3 cm
Included angle = 60°
Use the following formula:
![Area = \frac{1}{2}ab \times Sin(C)](https://tex.z-dn.net/?f=%20Area%20%3D%20%5Cfrac%7B1%7D%7B2%7Dab%20%5Ctimes%20Sin%28C%29%20)
Where,
a = 15.3 cm
b = 15.3 cm
C = 60°
Plug the values into the formula to find the area.
![Area = \frac{1}{2} \times 15.3 \times 15.3 \times Sin(60)](https://tex.z-dn.net/?f=%20Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%2015.3%20%5Ctimes%20%2015.3%20%5Ctimes%20Sin%2860%29%20)
![Area = \frac{1 \times 15.3 \times 15.3 \times Sin(60)}{2}](https://tex.z-dn.net/?f=%20Area%20%3D%20%5Cfrac%7B1%20%5Ctimes%2015.3%20%5Ctimes%20%2015.3%20%5Ctimes%20Sin%2860%29%7D%7B2%7D%20)
(3 S.F)