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A rhombus has 4 congruent sides, its diagonals bisect each other and are perpendicular between them.

If we know the length of the side, a, and the length of one of the diagonals, d1, we can find the area, A, of the rhombus which is:

A = (d1)[(1/2)(d2)]

How to find the one half of d2?

(1/2)(d2) = √[a^2 - [(1/2)(d1)]^2] = √[a^2 - (1/4)(d1)^2]

So,

A = (d1)[(1/2)(d2)]

A = (d1)√[a^2 - (1/4)(d1)^2]

A = √[(d1^2)[a^2 - (1/4)(d1)^2]]

A = √[(d1^2)(a^2) - (d1^4)/4]

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16y ago

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