Question

The surface area of a triangular pyramid is 96.6 square centimeters. The side lengths of the base are 6 centimeters, and the height of the base is 5.2 centimeters. What is the slant height?

Answer 1

Using the formula 1/2*b*h for the area of a triangle, we get 7.8 cm^2 as the area of the base. Now let us assume that the three faces of the pyramid are of the same dimensions. So by subtracting 7.8 from the total surface area and dividing by 3, we get a face area of 29.6 cm^2. We get a height of 19.73 cm (using a "base" of 3 cm). Using half of the face of the pyramid (a right triangle) and applying some trigonometry (19.73 cm/sin 60) we get 22.78 cm as the slant height of the pyramid.