SOLUTION: I have a hexagon with 6 equal sides! I have only one measurement that runs from the top vertex to the opposite vertex(diagonally)and is 15ft. I am to find the area of the hexagon

Question 104813: I have a hexagon with 6 equal sides! I have only one measurement that runs from the top vertex to the opposite vertex(diagonally)and is 15ft. I am to find the area of the hexagon in square feet. Can you please help. Thanks, Joann
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
A regular hexagon ha 6 equilateral triangles in it.
In this case each side is 15/2=7.5 feet
The altitude of one of the triangles divides it in half and is perpendicular to the base.
For one of these right angle triangles:
the base b=7.5/2=3.75
hypotenuse=c=7.5
altitude=a
a^2+b^2=c^2
a^2+3.75^2=7.5^2
a^2=7.5^2-3.75^2
a^2=56.25-14.0625
a^2=42.1875
a=6.49519 ft
area of any triangle=A=a*b/2
for one of the 6 equilateral triangles with sides of 7.5:
A=6.49519*7.5/2=24.357
Area of the regular hexagon=24.357*6= 146.142 sq ft.
Ed

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