# Geometry

A circle has a radius of 6 in. The inscribed equilateral triangle will have an area of: ?

1. 👍 0
2. 👎 0
3. 👁 767
1. i believe it would be 56.52 (not 100% positive though) because if the radius is 6, then the circumference would be 3.14(6^2)= 3.14(36) which is 113.04 then you would put that over 360 and set up a proportion:
113.04/360 = x/180 (simplified to 20347.2/360) which gives you a final answer of 56.52
hope this helps!

1. 👍 0
2. 👎 0
2. The height of the equilateral triangle will be a median in that triangle, and the centroid will be the centre of the circle.
That centroid splits the median in the ratio of 2 : 1
so the whole median, or the height of the triangle will be 9 in.
Half of the triangle will be a 30-60-90 triangle whose sides are in the ration of 1 : √3 : 2

9/√3 = b/1
so b = 9/√3 or the base is 18/√3

area of triangle = (1/2)(18/√3)(9) = 81/√3 or 27√3 or 46.765

Just thought of an easier way.

From the centre draw the 3 radii, giving us 3 congruent triangle with sides 6 and 6 and contained angle of 120°
Area of one of these = (1/2)(6)(6)sin120°
= 18(√3/2) = 9√3
but we have 3 of them, so the total equilateral triangle is 27√3

1. 👍 1
2. 👎 0

## Similar Questions

1. ### Math

An oblique triangle is inscribed in a circle. If one side of the triangle having a length of 10 cm and the angle subtended to that side is 20. Determine the area of the circle.

2. ### Math- HELP

There is a triangle inside of a circle. I have to find area of the shaded region which is the circle. So i would have to substract the area of the triangle from the area of the circle. the radius of the circle is 3 inches. I found

3. ### math

an equilateral triangle of side 20cm is inscribed in a circle calculate the distance of a side of the triangle from the centre of the circle

4. ### geometry

The perimeter of a triangle, its area, and the radius of the circle inscribed in the triangle are related in an interesting way. Prove that the radius of the circle times the perimeter of the triangle equals twice the area of the

1. ### geometry

An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. Then Write an expression for the inscribed radius r in

2. ### Geometry

A circle has a radius of 6 inches. The circumscribed equilateral triangle will have an area of:?

3. ### Geometry

Which step is the same when constructing an inscribed square and an inscribed equilateral triangle? A.Connect every arc along the circle. B.Construct a circle of any arbitrary radius. C.Set the compass width to greater than half

4. ### math

an equilateral triangle of side 10cm is inscribed in a circle. find the radius of the circle? show the solution

1. ### Math

An equilateral triangle is inscribed in a circle. Each side of the triangle has length x. What is the area of the circle? Please help

2. ### math

An equilateral triangle is inscribed in a circle. The radius of the circle is 21 in. Determine the side length of the triangle to the nearest 10th of an inch

3. ### Math

Check my answers please? There are only 10 The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X: The

4. ### Math

29. An equilateral triangle of side 10cm is inscribed in a circle. Find the radius of the circle