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Make a cut that goes diagonally across three adjoining faces of the cube. If a side of the cube is 's'. Each side of the triangle will square_root(2)*s.

Q: How can you cut a cube with one cut to obtain a equilateral triangle?

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An isosceles triangle

Yes. An equilateral triangle can be symmetrical because cut it straight down the middle and it will be symmertrical.

9

Obviously!! That is when you cut the equilateral triangle into two with the help of a line running from the top part of the triangle and stands perpendicular to the base of the triangle.

You would cut off a corner.

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An isosceles triangle

Yes. An equilateral triangle can be symmetrical because cut it straight down the middle and it will be symmertrical.

9

no, it looks like an equilateral triangle with the top cut off.

Obviously!! That is when you cut the equilateral triangle into two with the help of a line running from the top part of the triangle and stands perpendicular to the base of the triangle.

triangle

You would cut off a corner.

A 30-60-90 right triangle

A hexagon is a six-sided figure. Cut an equilateral triangle out of a piece of paper. Chop off little equilateral triangles at each tip of the triangle. What you have is a hexagonal piece of paper. Draw around it.

The picture shows you how... http://etc.usf.edu/clipart/38600/38659/trimid_38659_lg.gif

Cut it exactly down the middle, along its height, and put one piece aside. The remaining side is a right triangle. The slanting side of the right triangle is a whole side of the original equilateral triangle, the bottom is half of an original side, and the vertical line is the height of the original triangle. Now you have a right triangle and you know the lengths of two of its sides, so you use what you know about right triangles to find the length of the third side, which is the height of the original equilateral triangle. It turns out to be 0.866 times the side of the equilateral triangle. (rounded) Technically, that's (1/2) x (side) x sqrt(3)

The formula for area of a circle is Area=pi*radius2 you know the area of your circle so now find the radius. 154 = pi*r2 r = 7 cm if you can imagine the equilateral triangle in the circle imagine that the radius touches the exact center of this triangle and can extend to one of the three points on the triangle. (this next part would be so much easier if i could draw you a picture). now, if you remember that an equilateral triangle has three angles that each measure up to 60 degrees. if you take the radius of the circle and draw a line from the center of the triangle to the tip of the triangle you will actually cut on of the 60 degree angles in half. this would now make you have an angle 30 degrees. if you do this same thing to another point you will notice you actually have another triangle inside this triangle. since all triangle angles add up to 180 degrees you know all three angles of this new triangle. (note: this new triangle is not an equilateral triangle). so this new triangle has an angle 30 degrees, 30 degrees, and 120 degrees. you can now use the law of sines to find out the length of one side of the equilateral triangle. if you have drawn your picture correctly then you will see that one side of the new triangle actually shares one side of the equilateral triangle. if you look at your new triangle their is only one side that is known a known quantity. this side is the side that is shared with the equilateral triangle. use the law of sines to figure out the length of this side... 7 / sin(30) = x / sin(120) x = 12.12cm you now know that one side of the equlateral triangle is 12.12cm. since there is three sides to the triangle the total perimeter of the equilateral triange is 12.12 times 3 your answer for the perimeter of the equilateral triangle is 36.36cm