SOLUTION: What is the area of the largest equilateral triangle that can fit inside a cube
with an edge length of 10cm?
Algebra.Com
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?
....
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
RELATED QUESTIONS
What is the length of the side of the largest equilateral triangle that can
fit in a... (answered by richwmiller)
10) What is the area of the largest circle that will fit inside a square with an area of... (answered by nerdybill)
A boy draws an equilateral triangle PQR .He then drawn three perpendiculars from a point... (answered by ikleyn)
A circle can be inscribed in an equilateral triangle, each of whose sides has length... (answered by math_helper,ikleyn)
What is the radius of the largest circle that will fit inside a triangle that has two... (answered by ikleyn)
A square has an area of 32cm2
What is the area of the largest circle that can fit in it... (answered by MathLover1)
There is a circle inside a triangle the bottom of the triangle is 240 kilometers, one... (answered by stanbon)
What is the surface area or a cube with a edge length of 11 m? (answered by jim_thompson5910)
An equilateral is inscribed in a circle of radius 10cm. Find the area of the equilateral. (answered by edjones)