A pyramid is its base plus a triangle for every base edge, and each triangle uses the slant height, not the height. When only the height is given, the slant height comes from a right triangle with half the base edge. A triangular prism is two triangles plus three rectangles, one on each side of the triangle.
A square pyramid has base edge 10 and slant height 13. Find the surface area
The base is 10 by 10, which is 100.
Each triangle is half of 10 times 13, which is 65, and there are four.
100 + 260.
The answer is 360.
Where students go wrong
Using the height of the pyramid for the triangles. The triangles lean, so it is the slant height that runs down their middle.
Also called square pyramid surface area, slant height, triangular prism surface area or lateral area.
What you can put on this worksheet
Surface area of a pyramid
A square pyramid has base edge 7 and slant height 8. Find the surface area→ 161
Surface area of a triangular prism
A prism is 7 long, and its base is a right triangle with legs 5 and 12. Find the surface area→ 270
Questions about these worksheets
Yes. Every surface area of pyramids and prisms sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the surface area of pyramids and prisms questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: surface area of a pyramid and surface area of a triangular prism. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the height of the pyramid for the triangles. The triangles lean, so it is the slant height that runs down their middle.