The total area of all faces of a prism, found by adding the areas of the two bases and all lateral (side) faces.
Imagine unfolding a cereal box and laying it flat—you get a net of six rectangles. The surface area is the total area of that flattened cardboard. For any prism, you always have two identical bases plus a 'belt' of rectangles wrapped around the middle.
Showing a random 20 of 50 problems.
Example 1
easy
Find the lateral surface area of a prism whose base perimeter is 15 and height is 8.
Example 2
challenge
Among all closed rectangular boxes with surface area 96 cm2, which dimensions maximize the volume?
Example 3
easy
Find the lateral surface area of a rectangular prism with base perimeter 20 cm and height 7 cm.
Example 4
easy
A cube has surface area 150. Find its edge length.
Example 5
medium
If every edge of a cube is doubled, the surface area is multiplied by what factor?
Example 6
medium
If a cube's edge length is tripled, by what factor does the surface area change?
Example 7
challenge
Explain why two solids can have the same volume but very different surface areas, using a 1×1×8 box versus a 2×2×2 cube.
Example 8
medium
A triangular prism has a right-triangle base with legs 3 and 4 (hypotenuse 5) and length 10. Find its total surface area.
Example 9
easy
A prism has base area 12 and lateral surface area 50. What is its total surface area?
Example 10
medium
A rectangular prism has surface area 94 cm2 and base dimensions 3×4 cm. Find its height.Rect prism: base 3 × 4 cm, height h = ?
Example 11
easy
A cube of edge 10 cm: find the area of one face and the total surface area.Cube with edge 10 cm
Example 12
easy
A cube has side length 7 cm. Find its surface area.Cube with side length 7 cm
Example 13
easy
A cube has surface area 216 cm2. Find the edge length.Cube with unknown edge s; SA = 216 cm²
Example 14
medium
A swimming pool (rectangular prism, open top) is 10 × 6 × 2. Find the area to be tiled (bottom + four walls, no top).Open-top pool: 10 × 6 × 2 (no lid)
Example 15
easy
A rectangular prism (box) has length 5 cm, width 3 cm, and height 4 cm. Find its surface area.Rectangular prism: l = 5 cm, w = 3 cm, h = 4 cm
Example 16
medium
A triangular prism has right-triangle bases with legs 6 and 8 (hypotenuse 10) and length 12. Find its total surface area.
Example 17
easy
A triangular prism has two triangular bases each of area 6 and a lateral area of 40. Find the total surface area.
Example 18
hard
A box has volume 72 cm3 and a square base of side 3 cm. Find its surface area.Square-base box: side 3 cm, h unknown; V = 72 cm³
Example 19
easy
What is a 'net' of a prism?
Example 20
medium
A box is 5 × 5 × 10. Find its surface area.Box: 5 × 5 × 10