Worksheets · Geometry

Surface area of pyramids and prisms worksheet

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.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Surface Area of Pyramids and Prisms

Date Period

Find each lateral area, surface area or missing length.

  1. Use the surface area of a pyramid

    A square pyramid has base edge 6 and height 4. Find the surface area.
  2. A square pyramid has base edge 13 and slant height 13. Find the surface area.
  3. A square pyramid has base edge 24, and each lateral edge is 20. Find the surface area.
  4. A square pyramid has base edge 8 and height 3. Find the surface area.
  5. A square pyramid has base edge 14 and slant height 13. Find the surface area.
  6. A square pyramid has base edge 16, and each lateral edge is 17. Find the surface area.
  7. A square pyramid has base edge 11 and slant height 18. Find the surface area.

  1. Use the surface area of a triangular prism

    Each end of a prism is an isosceles triangle with sides 41,41 and 18, and its length is 28. What is its total surface area?
  2. A prism is 19 long, and its base is a right triangle with a leg 7 and hypotenuse 25. Find the surface area.
  3. A prism 28 long has ends that are each a right triangle with a leg 20 and hypotenuse 29. Find its surface area.
  4. Find the surface area of a prism of length 18 whose ends are each an isosceles triangle with sides 25,25 and 40.
  5. A tent shaped like a prism is 22 long. Its front is an isosceles triangle with sides 26,26 and 20. Find the surface area of the tent, floor included.
  6. A prism is 19 long, and its base is a right triangle with a leg 12 and hypotenuse 37. Find the surface area.
  7. Find the surface area of a prism of length 15 whose ends are each a right triangle with a leg 10 and hypotenuse 26.

  1. Use the lateral area of a pyramid

    A regular hexagonal pyramid has a base perimeter of 42 and slant height 14. Find the lateral area.
  2. How many side faces does a regular octagonal pyramid have? Each has area 44. Use that to find the lateral area.
  3. The base of a regular pyramid is a regular hexagon with sides of 2, and its slant height is 13. Find the lateral area.
  4. The perimeter of the base of a square pyramid is 36, and its slant height is 13. What is the lateral area?
  5. A regular octagonal pyramid has 8 congruent side faces, each of area 29. Find the lateral area.
  6. The base of a regular pyramid is a regular pentagon with sides of 2, and its slant height is 17. Find the lateral area.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Surface Area of Pyramids and PrismsAnswer keyVersion 1

Date Period

Find each lateral area, surface area or missing length.

  1. Use the surface area of a pyramid

    A square pyramid has base edge 6 and height 4. Find the surface area.96
  2. A square pyramid has base edge 13 and slant height 13. Find the surface area.507
  3. A square pyramid has base edge 24, and each lateral edge is 20. Find the surface area.1344
  4. A square pyramid has base edge 8 and height 3. Find the surface area.144
  5. A square pyramid has base edge 14 and slant height 13. Find the surface area.560
  6. A square pyramid has base edge 16, and each lateral edge is 17. Find the surface area.736
  7. A square pyramid has base edge 11 and slant height 18. Find the surface area.517

  1. Use the surface area of a triangular prism

    Each end of a prism is an isosceles triangle with sides 41,41 and 18, and its length is 28. What is its total surface area?3520
  2. A prism is 19 long, and its base is a right triangle with a leg 7 and hypotenuse 25. Find the surface area.1232
  3. A prism 28 long has ends that are each a right triangle with a leg 20 and hypotenuse 29. Find its surface area.2380
  4. Find the surface area of a prism of length 18 whose ends are each an isosceles triangle with sides 25,25 and 40.2220
  5. A tent shaped like a prism is 22 long. Its front is an isosceles triangle with sides 26,26 and 20. Find the surface area of the tent, floor included.2064
  6. A prism is 19 long, and its base is a right triangle with a leg 12 and hypotenuse 37. Find the surface area.2016
  7. Find the surface area of a prism of length 15 whose ends are each a right triangle with a leg 10 and hypotenuse 26.1140

  1. Use the lateral area of a pyramid

    A regular hexagonal pyramid has a base perimeter of 42 and slant height 14. Find the lateral area.294
  2. How many side faces does a regular octagonal pyramid have? Each has area 44. Use that to find the lateral area.352
  3. The base of a regular pyramid is a regular hexagon with sides of 2, and its slant height is 13. Find the lateral area.78
  4. The perimeter of the base of a square pyramid is 36, and its slant height is 13. What is the lateral area?234
  5. A regular octagonal pyramid has 8 congruent side faces, each of area 29. Find the lateral area.232
  6. The base of a regular pyramid is a regular pentagon with sides of 2, and its slant height is 17. Find the lateral area.85

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A square pyramid has base edge 10 and slant height 13. Find the surface area

  1. The base is 10 by 10, which is 100.
  2. Each triangle is half of 10 times 13, which is 65, and there are four.
  3. 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
The base of a pyramid is a square with side 7. Each of its four triangular faces has base 7 and height 10. Find the surface area. → 189
Surface area of a triangular prism
A prism 8 long has ends that are each an isosceles triangle with equal sides 17 and base 16 (height 15). Find its surface area. → 640
Trapezoidal, pentagonal and hexagonal prisms
Find the surface area. The base is a regular hexagon. — a regular hexagonal prism, labeled 6, 5.2, 8 → 475.2
Pentagonal and hexagonal pyramids
Find the surface area. The base is a regular hexagon. — a regular hexagonal pyramid, labeled 8, 6.9, ℓ = 5 → 285.6
Lateral area of a pyramid
Each side face of a square pyramid has an area of 31. Find the lateral area. → 124
Lateral area of a prism
The prism stands on its base: the top and bottom faces are the bases. Find the lateral area. — a rectangular prism 2 by 6 by 8 → 128
Rhombus and trapezoid prisms, a pyramid from its base height
A prism has a trapezoid base with parallel sides 10 and 16, a height of 8, and legs 8 and 10. The prism is 4 long. Find its surface area. → 384

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 7: surface area of a pyramid, surface area of a triangular prism, trapezoidal, pentagonal and hexagonal prisms, pentagonal and hexagonal pyramids, lateral area of a pyramid, lateral area of a prism and rhombus and trapezoid prisms, a pyramid from its base height. 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.