Mega easy question on surface area?

Question

There's this piece of crystal,with 2 right square pyramids at both ends of a prism.The height of the whole crystal is 54cm.Side of square of pyramid is 16cm and height of prism though it looks more cuboid) is 24cm.Find the surface area.

Well,basically the diagram consist of one cuboid with 2 pyramids at the ends.

Answer 1

Assuming the two pyramids are identical, their common height is (54-24)/2 = 15cm

We need the height of a triangular side of the pyramids. Look at the picture on this page for reference: http://mathworld.wolfram.com/SlantHeight...

We know that h=15, and r is half the side of the square, so r=8. By the Pythagorean Theorem,

s² = h² + r² = 225 + 64 = 289

so s = 17

Area of a triangle = ½(base)(height) = ½*16*17 = 136 cm²

There are 8 of these triangles, so their total area = 1088 cm²

The lateral area of the prism consists of 4 rectangles that are each 24cm × 16 cm, so the total area from these rectangles is 4*24*16 = 1536 cm²

Thus, the total surface area is 1088 + 1536 = 2624 cm²