Question

5. Find the area of an equilateral triangle with radius 8 m. Leave your answer in simplest radical form.

Answer 1

Radius,r=8√3 m

Height of triangle ,h=2r ⇒ 16√3 m

Side of the triangle ,a=16√3/sin60 ⇒ 32 m

Area of the triangle,

A=√3/4(a²)

A =√3/4(32²)

A =443.4 m²

Answer 2

Answer:

The area of an equilateral triangle is $83.13m^2$.

Step-by-step explanation:

Given: The radius of an equilateral triangle is 8m.

To find: The area of an equilateral triangle.

Solution: It is given that the radius of an equilateral triangle is 8m.

Now, height of the triangle is given as:

$h=2r$

Substituting the value of r, we have

$h=2(8)$

$h=16m$

The side of the triangle is given as:

$a=hsin(60^{\circ})$

$a=16(sin60^{\circ})$

$a=16(\frac{\sqrt{3}}{2})$

$a=8\sqrt{3}m$

Now, the area of an equilateral triangle is given as:

$Area=\frac{\sqrt{3}}{4}(a^2)$

$Area=\frac{\sqrt{3}}{4}(8\sqrt{3})^2$

$Area=\frac{\sqrt{3}}{4}{\times}64{\times}3$

$Arae=48\sqrt{3}m^2$

$Area=83.13m^2$

Therefore, the area of an equilateral triangle is $83.13m^2$.