Answer:
[tex] Area = 101.4 cm^2 [/tex] (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 = [tex] \frac{48}{\pi} [/tex] = 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:
[tex] Area = \frac{1}{2}ab \times Sin(C) [/tex]
Where,
a = 15.3 cm
b = 15.3 cm
C = 60°
Plug the values into the formula to find the area.
[tex] Area = \frac{1}{2} \times 15.3 \times 15.3 \times Sin(60) [/tex]
[tex] Area = \frac{1 \times 15.3 \times 15.3 \times Sin(60)}{2} [/tex]
[tex] Area = 101.4 cm^2 [/tex] (3 S.F)
