# The height BH of the rhombus ABCD divides its side AD into segments AH = 4 and HD = 1. Find the area of the rhombus

May 31, 2020 | Education

| The area of the rhombus is S = ah, where a is the side of the rhombus, h is the height of the rhombus.

AD = AH + HD = 4 + 1 = 5.

AD = AB = BC = CD (by definition of a rhombus).

Consider the triangle ABH.

ABH is rectangular (because BH is height), then by the Pythagorean theorem: AB ^ 2 = BH ^ 2 + AH ^ 2

5 ^ 2 = BH ^ 2 + 4 ^ 2

25 = BH ^ 2 + 16

BH2 = 9

Bh = 3

S diamond = AD * BH = 5 * 3 = 15

Answer: S diamond = 15

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