A right pyramid has a regular hexagon as a base. The slant height is 20, and the perimeter of its base is 10. What is the lateral surface area of the pyramid?
Each side of the pyramid is a triangle and all these triangles are congruent.
We can find the lateral surface area by finding the area of one of the triangles and multiplying by the number of trianges.
The base of each triangle is 10 divided by 6, which gives us 5/3.
The height of each triangle is 20.
The area of each triangle is: A = ½·base·height = ½·(5/3)·20 = 50/3.
The total surface area is: 6·(50/3) = 100.
You might notice that another way to get your answer would be to use the formula: A = ½·perimeter·height.