Find Surface area and volume of a right pyramid with a square base?

Question

I am only given the height, which is 8, and the length of one side of the square base, which is 12. I need to find the surface area and volume. I would include a picture but I don't know how.

Answer 1

Voume is easiest: V= (1/3)hB where B=area of the base or 12x12=144

V=(1/3)(144)(8) = 48x8 =384 cubic units

Area is the base area + 4 times the area of each of the 4 triangular sides

base area = B = 12x12 = 144

each triangular side =(1/2) base times height. the base is 12. The height is the hypotenuse of a right triangle with sides 8 and (1/2)12, or 8 and 6. 8 and 6 makes the hypotenuse 10. It's a 3-4-5 triangle, doubled, which is a 6-8-10 right triangle

That makes each of the 4 sides = (1/2)(12)(10) = 60. Four sides makes the side areas total 4x60=240

Add that to the base area for total surface area: 240 + 144 = 384