A rectangular prism measures 7 ft by 8 ft by 6 ft. Find both volume and surface area.
Show reasoning / computation: __________________________________________
CCSS 7.G.B.6 · volume & surface area of right prisms
Surface Area and Volume of Right Prisms Worksheets
Connect base area, prism length, volume, and total surface area. Foundation sets stay with rectangular prisms; later sets can introduce right triangular prisms with all required dimensions supplied.
Preview · US Letter
Surface Area & Volume of Right Prisms
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
A right triangular prism has an isosceles triangular base with base 8 cm, height 4 cm, equal sides 5.66 cm, and prism length 7 cm. Find volume and surface area.
Show reasoning / computation: __________________________________________
Problem 3
A right triangular prism has an isosceles triangular base with base 4 ft, height 6 ft, equal sides 6.32 ft, and prism length 4 ft. Find volume and surface area.
Show reasoning / computation: __________________________________________
Problem 4
A right triangular prism has an isosceles triangular base with base 4 in, height 4 in, equal sides 4.47 in, and prism length 7 in. Find volume and surface area.
Show reasoning / computation: __________________________________________
Problem 5
A right triangular prism has an isosceles triangular base with base 6 ft, height 8 ft, equal sides 8.54 ft, and prism length 7 ft. Find volume and surface area.
Show reasoning / computation: __________________________________________
Problem 6
A right triangular prism has an isosceles triangular base with base 8 in, height 8 in, equal sides 8.94 in, and prism length 9 in. Find volume and surface area.
Show reasoning / computation: __________________________________________
Problem 7
A right triangular prism has an isosceles triangular base with base 6 cm, height 6 cm, equal sides 6.71 cm, and prism length 4 cm. Find volume and surface area.
Show reasoning / computation: __________________________________________
Problem 8
A rectangular prism measures 5 in by 6 in by 4 in. Find both volume and surface area.
Show reasoning / computation: __________________________________________
Volume and surface area from the base
Every right prism has a base and a length. Volume is base area times length, while surface area is the two bases plus a set of rectangular faces whose combined area equals the perimeter of the base times the length. Foundation sets use rectangular prisms and later sets add right triangular prisms.
Confusions worth naming
- Leaving out one or both bases when adding faces.
- Writing square units for volume or cubic units for surface area.
- Using the slant of a triangular base as the prism length.
One rectangular and one triangular prism
- A rectangular prism 5 by 3 by 4 has volume 60 cubic units and surface area 2(15 + 20 + 12) = 94 square units.
- A right triangular prism with a 3-4-5 base and length 10 has base area 6, so its volume is 60 cubic units. Its surface area is 2 × 6 + (3 + 4 + 5) × 10 = 132 square units.
Making the difference concrete
A cereal box or a folded paper net helps students see why volume counts filling the solid while surface area counts covering it. Ask them to sketch the net of a triangular prism before computing, so all five faces are accounted for.
Note 1
Volume of a right prism is base area times prism length/height.
Note 2
Surface area includes both bases plus every lateral face.
Note 3
Example: a right triangular prism with base area 6 and length 10 has volume 60 cubic units; its surface area is the two triangular bases plus the three rectangular lateral faces.
Note 4
Volume uses cubic units; surface area uses square units.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Quick answers
Do these include cylinders?
No. This Grade 7 route stays with cubes and right prisms; cylinder volume belongs to later standards.
Do triangular-prism problems give enough information?
Yes. The base, base height, equal side lengths, and prism length are all supplied so surface area is determinate.
Which standard does this practice?
CCSS 7.G.B.6: solve problems involving volume and surface area of three-dimensional objects composed of cubes and right prisms.