how would you find the surface area of a triangular pyramaid with side lenghts of 4in, 4in, and 7in

Question

anonymous · Answer

the triangular pyramid is composed of 4 triangles and 1 square. so split them up and calculate it individually, then add the surface area together to get the total of the area.
For the triangles:
both sides are 4 and base is 7. Split this up into two 90 degree triangles. We have the side, and the base, so we calculate the height by using Pythagorean's theorem. $$a ^{2}*b ^{2}=c^{2}$$ 
3.5^2 + b^2 = 4^2
b = 1.94
The formula for 90 degree triangle is [base*height]/2.
so (3.5*1.94)/2 = 3.395in^2
now multiply this by 8 since there are eight 90 degree triangles.
3.395 * 8 = 27.16
we are left with the square to calculate. the surface area for the square is simply 7 * 7 = 49.
we add it all up, 27.16 + 49 = 76.16 in ^2

anonymous · Answer

sorry, i was thinking of a pyramid not a triangular pyramid. You just need to subtract the surface area of two of the 90 degree triangles. and replace the surface area of the square with a triangle. the triangle will have all sides 7 so use pythagorean's theorem again to calculate the surface area.