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Question: The area of the equilateral triangle, in which three coins of radius 1 cm are placed as shown in the...

The area of the equilateral triangle, in which three coins of radius 1 cm are placed as shown in the figure, is

A

6 + 434 \sqrt { 3 }

B

434 \sqrt { 3 }–6

C

7 +434 \sqrt { 3 }

D

434 \sqrt { 3 }

Answer

6 + 434 \sqrt { 3 }

Explanation

Solution

Side of equilateral triangle 3\sqrt { 3 } + 2 + 3\sqrt { 3 } (by trigonometry)

A = (side)2 34\frac { \sqrt { 3 } } { 4 }