Question

The diagram shows a circle and an equilateral triangle. One side of the equilateral triangle is a diameter of the circle. The circle has a circumference of 48cm. Work out the area of the triangle.

Answer 1

Answer:

$Area = 101.4 cm^2$ (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 = $\frac{48}{\pi}$ = 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:

$Area = \frac{1}{2}ab \times Sin(C)$

Where,

a = 15.3 cm

b = 15.3 cm

C = 60°

Plug the values into the formula to find the area.

$Area = \frac{1}{2} \times 15.3 \times 15.3 \times Sin(60)$

$Area = \frac{1 \times 15.3 \times 15.3 \times Sin(60)}{2}$

$Area = 101.4 cm^2$ (3 S.F)