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Stells [14]
3 years ago
15

PLZ HELP ASAP WILL MARK BRAINLIEST

Mathematics
1 answer:
RSB [31]3 years ago
3 0

Answer:

72\sqrt{3}

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = \frac{1}{2} × d₁ × d₂ (d₁ and d₂ are the diagonals )

The diagonals bisect each other at right angles

d₁ = 2 × 6 = 12

Use the tangent ration in the upper left right triangle and the exact value

tan60° = \sqrt{3}

tan60° = \frac{opposite}{adjacent} = \frac{opp}{6} = \sqrt{3} ( multiply both sides by 6 )

opp = 6\sqrt{3} , then

d₂ = 2 × 6\sqrt{3} = 12\sqrt{3}

Thus

A = \frac{1}{2} × 12 × 12\sqrt{3} = 6 × 12\sqrt{3} = 72\sqrt{3}

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