Question

A pyramid has a rectangular base with edges of length 10 and 24. The vertex of the pyramid is directly 13 units above the center of the base. What is the: Total surface area of the pyramid?​

Answer 1

10 x 24 x 13 = 3120?

Explanation:

I hope this is right!

Answer 2

`10√(313) +24√(194)+240` square units

Explanation:

If your base is 10x24, and the vertical height is 13, you first have to find the slant height of the pyramid, in other words, calculate the hypotenuse of the triangles constructed using the height and the base divided by 2. You will need to find two slant heights as the base is not square. If you look at that image, the slant heights are marked in blue, and the specific measurements know are given in red. Using that, we can apply the Pythagorean theorem to determine the slant heights, which are
`√(194)` and
`√(313)`, then we need to calculate the area of each triangular face. Thus they are
`5√(313)` and
`12√(194)`, but there are two identical faces in the pyramid, which means we should double the area of the faces to achieve
`10√(313) +24√(194)`, then we need to simply add the base as it's a face. So the answer is
`10√(313) +24√(194)+240`