SOLUTION: Find the volume, to the nearest tenth, of a pyramid that is 6 feet tall and whose base is an equilateral triangle with sides each 10 feet long????

Question 146296: Find the volume, to the nearest tenth, of a pyramid that is 6 feet tall and whose base is an equilateral triangle with sides each 10 feet long????
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
V=1/3BH
FIRST WE FIND THE BASE AREA.
WE CONSTRUCT 2 RIGHT TRIANGLES BY DRAWING A PERPENDICULAR LINE FROM ONE CORNER TO THE CENTERER OF THE OPPOSITE SIDE. ONE SIDE OF THESE TRIANGLES IS 5 FEET & THE HYPOTENUSE IS 10 FEET.
USING THE PYTHAGOREAN THEOREM A^2+B^2=C^2 WE GET:
5^2+x^2=10^2
25+X^2=100
X^2=100-25
X^2=75
X=SQRT75
X=8.66 FOR THE HEIGHT.
AREA OF 2 TRIANGLES=2*5*8.66=86.6 FT^2.
V=1/3*86.6*6
V=519.6/3
V=173.2 FT^3

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