Question #2b63f

1 Answer
Parabola
Jan 9, 2018

See below.

Explanation:

Let's say we have a rhombus like one below.

First of all, if we know the length of one side, then we know the length of all the others. We name the length #s#.
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Second, we have our diagonal #d#.

We could view this as two separate triangles separated by the diagonal.
Esentially, we could add the areas of these two triangles.

We use Heron's formula: # A=sqrt(s*(s-a)*(s-b)*(s-c))#
where #a,b,c# are the length of the sides of the triangle and #s# is the semi perimeter.

We see that both of the triangles have the side lengths of #s,s,d#

Using heron's formula, we have:
#A=2(sqrt(((2s+d)/2)*((2s+d)/2-s)*((2s+d)/2-s)*((2s+d)/2-d)))#

We are multiplying by 2 because both of the two triangles have the same side lengths.
You could plug the values in this to find your answer.

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