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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:
Where,
a = 15.3 cm
b = 15.3 cm
C = 60°
Plug the values into the formula to find the area.
(3 S.F)