Find Total surface area of the pyramid

Question

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?

Answer 1

Getting the area of the base you would just do 10 x 24. The area of each of the triangles is a bit harder to see. We'll consider one of the triangles with base 10. To get the height of the triangle, which we'll denote as H, you would have to construct a right triangle standing up inside the pyramid. It has a height of 13 and base of 24/2 = 12. The hypotenuse of this triangle is H. So H is √(12² + 13²) and to get the area of the first surface triangle, do 1/2 * 10 * √(12² + 13²). Hope you can visualize this.