Question

How do you find the area of a rhombus using its perimeter?

Answer 1

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Area `= (p^2 sin theta)/16`

where `p` is the length of the perimeter and `theta` is one of the internal angles of the rhombus.

Explanation:

If the perimeter is of length `p` then the area is anywhere in the range `0` to `(p/4)^2 = p^2/16`
If the perimeter is of length `p` then the length of one side is `p/4`.

If we place one side of the rhombus horizontally, then the area is equal to the product of the base and height, The base is of length `p/4` and the height is `p/4 sin theta`, where `theta` is an internal angle of the rhombus.

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