Question

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

Answer 1

The area of a rhombus is `E=1/2 * (d1 * d2)` where `d1` and `d2` are the diagonal lengths of the rhombus.

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).

From Pythagorean Theorem you get :

#7.5 ^2 + d1^2 = 11^2=> d1^2 = 64.75=> d1 = 8.046# approximately.

That means the other diagonal is `2 * 8.046 = 16.092` units long.

So the area is `E=(d1 * d2) / 2 = 15 * 16.092 / 2 = 120.67`.