The lateral area of a pyramid is L.A.= 12Pl, where P is the perimeter of the base and l is the slant height of the pyramid.
See solution.
Practice makes perfect
We are told that the lateral area of a pyramid with a square base is L.A.=240 square feet. Its base edges are s=12 feet long.
We are asked to find the height of the pyramid. First let's use the formula for the lateral area, L.A.= 12Pl, where P is the perimeter of the base and l is the slant height of the pyramid. Since the base is a square, its perimeter is P=4* 12=48 feet. Now, let's find l!
Finally, we found that the height of the pyramid is AC=8 feet. We are also asked to answer two questions.
What additional information do you know about the pyramid based on the given information?
From the given information we know, for instance, that lateral faces are congruent, isosceles triangles. From the given information we can find its height, and after that we could find its surface area, base area, volume, and many other things.
How can a diagram help you identify what you need to find?
Thanks to the diagram, we identify a right triangle that helps us find the height of the pyramid using the Pythagorean Theorem.
