The area of an equilateral triangle

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Question from michael, a parent:

my daughter has been given a task and I'm stuck too.
if an area of an equilateral triangle = 85cm squared there are no other dimensions provided.
how do I calculate the length of each side ? please

Hi Michael,

Suppose the length of each side of the triangle is b cm. The area of a triangle is half the base times the height so if the height is h cm then

85 = 1/2 b h.

triange

The angle at each vertex has measure 60 degrees and hence sin(60^o) = h/b so h = b sin(60^o). Thus

85 = 1/2 b h = 1/2 b × b sin(60^o)

Solve for b.

Penny

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