bz, cx and ay are heights of the equilateral triangle abc drawn above. If from b down to intersecting point of the heights is 4 square root 3, what is the area of the triangle abc?

Question

anonymous · Answer

side of equiltera triangle = 2/sqrt(3)  * height of equilateral triangle 
area of equilateral triangle =sqrt(3)/4  * (side of equilateral triangle )^2

anonymous · Answer

here height of equilateral triangle =4*sqrt(3)
hence first calculate side and then calculate are using the fromula baove

anonymous · Answer

If from b down to intersecting point of the heights is 4 square root 3, so  here the height is not  full, but till the point, so  is 4*sqrt(3) half of the height???

anonymous · Answer

side of equiltera triangle = 8 
8^2*sqrt(3)/4= 16sqrt(3)

anonymous · Answer

oops i didn't read the question completely and assumed the height as  4*sqrt(3)
for equilateral triangle the heights intersect at the centroid .
centroid here divides the heights in the ratio of 2:1 (in general for any  triangles centroid always divides medians in the ratio of 2:1)
so here  2/3 * height = 4*sqrt(3)
hence height =3/2 * 4*sqrt(3)