if a circle has a radius of 6 inches,what will the area of the circumscribed equilateral triangle be?
To find the area of the circumscribed equilateral triangle, we need to calculate the length of its side first. The side length of an equilateral triangle inscribed in a circle is equal to the diameter of the circle.
Since the radius of the circle is given as 6 inches, the diameter will be double that, which is 12 inches. Therefore, each side of the equilateral triangle will also be 12 inches.
To find the area of an equilateral triangle, we can use the formula:
Area = (side length^2 * √3) / 4
Plugging in the side length of 12 inches into the formula, we get:
Area = (12^2 * √3) / 4
Now, let's calculate the area:
Area = (144 * √3) / 4
To simplify the expression, we can divide both the numerator and denominator by 4:
Area = 36 * √3
So, the area of the circumscribed equilateral triangle will be 36√3 square inches.
Make a sketch
Draw a radius to each of the sides, it will meet it at right angles and bisect the sides
Draw lines from the centre to each of the vertices.
You should have 6 triangles with angles 30,60 and 90
one of the sides will be 6
I can find the other side of one of those triangles.
tan 30 = 6/x
1/√3 = 6/x
x = 6√3
so the area of one of those triangles = (1/2)(6√3)(6)
= 18√3
so the area of the whole big triangle is 6(18√3) = 108√3