# Geometry

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Find the area of the rhombus: In rhombus ABCD, AB=11 and AC=13. Find the area of the rhombus.

What should be done to find the values of the diagonals?

• Geometry -

A = D1*D2/2 = 13 * 13 / 2 =84.5

All of the sides of a rhombus are equal. So the longest side is the diagonal.

• Geometry -

CORRECTION!

The 2 diagonals are NOT equal. But they
are perpendicular bisectors of each other. They intersect at E.

(AE)^2 + (BE)^2 = (11)^2,
(6.5)^2 + (BE)^2 = 121,
42.25 + (BE)^2 = 121,
(BE)^2 = 121 - 42.25 = 78.75,
BE = sqrt(78.75) = 8.9.

BD = 2 * BE = 2 * 8.9 = 17.8.

A = D1 * D2 / 2 = 13 * 8.9 / 2 = 57.85

• Geometry -

OOPS!

A = D1 * D2 / 2 = 13 * 17.8 /2 = 115.7

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