Examine the figure and decide which colored area is the largest among others, or are they all the same?
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Thank you for sharing your solution.
Each triangle is congruent!
From the figure, we see that for 1 green triangle, there is 1 blue triangle and 1 orange triangle.
Hence, All the areas are same.
Thank you for sharing your solution.
Area of one blue equilateral triangle is : 4 3 ( 1 2 ) ⟹ Area of 6 blue triangles is: 2 3 3
Area of the regular hexagon of side 1 : 2 3 3
Area of one isosceles Green triangle of non-base side 1 is : sin 1 2 0 ∘ 2 3 × 2 1 × 1 2 = 4 3 ⟹ Area of 6 Green is : 2 3 3
All Areas are Equal
Formulas used: ( s = 1 )
Area of an equilateral Triangle: 4 3 s 2
Area of an Isosceles Triangle: 2 1 s 2 sin ( 1 2 0 ∘ )
Area of a regular hexagon: 2 3 3 s 2
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