Question 320168: What is the area of the largest equilateral triangle that can fit inside a cube
with an edge length of 10cm?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! What is the area of the largest equilateral triangle that can fit inside a cube
with an edge length of 10cm?
equilateral triangles are 2 dimensional figures with area not volume,
cubes are 3 dimensional figures with volume not area, maybe do you mean the area of the largest equilateral triangle that can fit inside a square with edge length of 10 cm? or do you mean a regular tetrahedron (a 3 dimensional solid that is made of 4 equilateral triangles that form a triangular pyramid) ? if I or anyone else answers this in a way you did not intend perhaps you should repost?
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let's do the largest equilateral triangle that can fit inside a square with edge length of 10 cm:
1 - 1 - 1 equilateral triangle is made up of 2 right triangles of 30-60-90 and the height of these 2 right triangles is the side opposite to the 60 degree angle -->
sin 60 = opp/hyp = opp/1 = sqrt(3)/2 = height of a 1-1-1 equilateral triangle,
if base of the equilateral triangle is 10, then the height would be:
10 * sqrt(3)/2 = 5sqrt(3) = approx. 8.66 which is not quite the height of the square, and the area would be:
1/2 * 10 * 5sqrt(3) = 5 * 5sqrt(3) = 25sqrt(3) = approx. 43.3 square cm is the area of the largest equilateral triangle that can fit inside this square
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