What is the area of the blue rectangle?

Geometry Level 2

Eight identical circles, each of radius one unit are arranged in a blue rectangle as shown. What is the area of the blue rectangle?

3 12 + 12 3\sqrt{12}+12 6 2 + 3 6\sqrt{2}+\sqrt{3} 6 ( 2 3 − 2 ) 6(2\sqrt{3}-2) 12 3 + 12 12\sqrt{3}+12

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1 solution

Hassan Abdulla
Feb 24, 2018

The triangle is equilateral so h = 4 2 − 2 2 = 2 3 h=\sqrt { 4^2-2^2 } =2\sqrt { 3 }

the height of the rectangle is h + 2 = 2 3 + 2 h+2=2\sqrt { 3 }+2

the width the rectangle is 6

the Area is 6 × ( 2 3 + 2 ) = 12 3 + 12 6\times \left( 2\sqrt { 3 } +2 \right) =12\sqrt { 3 } +12

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