A Hexagon and a Triangle
Geometry
Level
2
A regular hexagon and an equilateral triangle have the same perimeter of 24 units, what is the ratio of the area of the triangle to the area of the hexagon? Express as a common fraction.
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1 solution
The equilateral triangle which has a perimeter of 24 units would have each side as 8 units. So area of triangle would be 4 r o o t 3 x 8 x 8.
A hexagon is made of 6 EQUILATERAL TRIANGLES as shown in the figure below. .
According to data perimeter of hexagon is 24 units so its edges would be 4 units each..! Therefore edge of each smaller equilateral triangle inside the hexagon is 4 units.
So we find the area of hexagon by finding the area of the smaller equilateral triangle inside hexagon and multiply it by 6.
Area of the hexagon = Area of each smaller equilateral triangle * 6 = 4 r o o t 3 x 4 x 4 x 6.
The ratio of AREA OF TRIANGLE to AREA OF HEXAGON is clearly 2/3