Question

The shorter diagonal of a rhombus is equal in length to one of its sides. The length of a side is 6 inches. What is the area of the rhombus in simplest radical form?

Answer 1

Step-by-step explanation:

Let BD is Short diagonal, then

BO = DO = 3 cm (diagonals are perpendicular bisectors)

AO = CO

angle BOC = 90°

Therefore,

${co}^{2} = {6}^{2} - {3}^{2}$

$co = \sqrt{36 - 9}$

$co = 3 \sqrt{3}$

Therefore,

$ac = 6 \sqrt{3}$

Area of Rhombus = 1/2 × d1 × d2

$area = (1 \div 2) \times 6 \times 6 \sqrt{3}$

$area = 18 \sqrt{3}$

And, Happy to Help!