Find the surface area and volume of the solid pictured below which is the composite of a right rectangular?

Question

Find the surface area and volume of the solid pictured below which is the composite of a right rectangular prism and a square pyramid with a height of 3.

http://tinypic.com/view.php?pic=85lnfav&s=1

Answer 1

The hardest part is of course the top.

The bottom will be 3² = 9
Each rectangular face will be 3 x 6 = 18. Four faces = 72
Now the triangles, the base of the triangle is 3. The slant height you have to figure using the Pythagorean theorem.

The height is 3
The distance to the triangle 3/2 = 1½.
So the slant height will be the hypotenuse of this:
a = 3, b = 1.5, c = ?
a² + b² = c²
3² + 1.5² = c²
9 + 2.25 = c²
c = sqrt(11.25)
c = 3.354

So for the triangle ½ x base x height
base = 3, height = 3.354

Area of a triangle = 5.03 sq. units
Four faces = 20.12.

Adding it all up:
base = 9
4 sides = 72
4 triangles = 20.12
101.12 sq. units