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I need help finding the height of a rhombus?
Its diagonals are 18 and 80 my notes aren't helping me at all, could someone take me through the steps? I don't want just the answer.
1 Answer
- CalibanLv 71 decade agoFavorite Answer
The diagonals bisect; thus, they are perpendicular. So, there has to be four triangles within the rhombus. The triangles legs are ½ your given measures: 18/2 = 9 and 80/2 = 40.
Now use the Pythagorean Theorem to find the base (hypotenuse) of the rhombus. 9²+40²=1681; √1681 = 41; this is one of the Pythagorean Triples: 9, 40, 41.
41 is your base measure.
Area = ½(d1)(d2) which is ½(9)(40) which is ½(360) = 180.
Now that you have the area you can use this formula: Area = base•height
A = bh; 180 = 41h; 180/41 = h; 4.39 ≈ h.
