# The side of the rhombus is 8, and the distance from the center of the rhombus to it is 2. Find the area of the rhombus

May 31, 2020 | Education

| Denote the key points as shown.

Draw an extension of the height OE to side AB and denote the intersection point as F

The area of the rhombus (as well as the parallelogram) is equal to the product of the height on the side of the rhombus.

Rhombus height = EF (because EF is perpendicular to CD). Consider the triangles DOE and BOF.

DO = OB (by the second property of the rhombus)

∠DOE = ∠BOF (as they are vertical)

∠EDO = ∠FBO (as these are internal cross-lying)

Therefore, the triangles DOE and BOF are equal in the second feature.

Then OE = OF => EF = 2 * OE = 2 * 2 = 4

S diamond = EF * CD = 4 * 8 = 32

Answer: S rhombus = 32

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