SOLUTION: What is the: Total surface area of the pyramid? 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

Algebra ->  Surface-area -> SOLUTION: What is the: Total surface area of the pyramid? 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       Log On


   

Question 1175949: What is the: Total surface area of the pyramid?
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?
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
V = 1/3(B)(h)

(the volume of a pyramid is 1/3 times the area of the base times the height)

V+=+1%2F3+%2A+%2810+%2A+24%29+%2A+%2813%29

V+=+1040

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are four triangular faces and the rectangular base.

The area of the base is simple; I leave that to you.

Two of the triangular faces have bases of length 24. The heights of those triangles are the hypotenuses of right triangles with legs 5 (half the length of the shorter side of the base) and 13 (the height of the pyramid).

The other two triangular faces have bases of length 10; the heights of those triangles are the hypotenuses of right triangles with legs 12 (half the length of the longer side of the base) and 13 (the height of the pyramid).

I leave the rest of the calculations to you.

Use the Pythagorean Theorem to find the heights of the triangular faces; use those heights and the bases of the faces to find the areas of the faces; and find the sum of the areas of the four faces and the base.