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Question

In rhombus ABCD, AB = 11 and AC = 15. What is the area of the rhombus?

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Solution

The area of a rhombus is E=12(d1)(d2) where d1 and d2
The one diagonal is AC=15.
We have to do is find the length of the other diagonal. If you connect both sets of opposite corners of the rhombus, you should get a "diamond" divides into four equal triangles. One of these triangles has hypotenuse $11$
(the side AB). The diagonal lines cut each other exactly in half, so the resulting triangle has hypotenuse $11$
and one side length 7.5 (half of 15). are the diagonal lengths of the rhombus.
7.52+d21=112
d21=64.75
d1=8.046
That means the other diagonal is 2×8.046=16.092 units long.
So the area is E=1215×16.092=120.67

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