Stage 8 - Q1 - 2 marks
A right triangle has perpendicular sides 3 cm and 4 cm. Find the total area of two such triangles.
Hint
A closed prism has two triangular ends.
Stage 8 - Q2 - 2 marks
A triangular prism has cross-section sides 3, 4 and 5 cm and length 6 cm. Find the total area of its three rectangular faces.
Hint
Each cross-section side is the width of one rectangle.
Stage 8 - Q3 - 2 marks
A prism has three rectangular faces of total area 72 cm² and two triangular ends of area 6 cm² each. Find its total surface area.
Hint
Add all five faces.
Stage 8 - Q4 - 2 marks
A closed prism has right triangular cross-section sides 6, 8 and 10 cm and length 5 cm. Find its surface area.
Hint
Separate triangular ends and rectangular sides.
Stage 8 - Q5 - 3 marks
A tube of length 9 cm has triangular cross-section sides 5, 12 and 13 cm. Both ends are open. Find the material area.
Hint
Do not include faces that are absent.
Stage 8 - Q6 - 3 marks
A closed prism with cross-section sides 3, 4 and 5 cm has length 10 cm. The 4 cm by 10 cm face is glued to a board. Find the exposed area.
Hint
The two triangular ends are still exposed.
Stage 8 - Q7 - 4 marks
A right triangular prism with cross-section sides 3, 4 and 5 cm has total surface area 156 cm². Find its length.
Hint
Only the three rectangular faces depend on the prism length.
Stage 8 - Q8 - 4 marks
Two identical closed triangular prisms, with cross-section sides 3, 4 and 5 cm and length 5 cm, are joined end to end. Find the exterior surface area.
Hint
A shared face is counted twice in the separate totals.
Stage 8 - Q9 - 5 marks
A prism of length 10 cm has a triangular cross-section with area 12 cm² and perimeter 18 cm. Find its volume and surface area. Explain why the answers use different units.
Hint
The same cross-section gives an area for volume and a perimeter for side faces.
Stage 8 - Q10 - 6 marks
A prism with right triangular cross-section sides 3, 4 and 5 cm and length 12 cm is cut into three equal shorter prisms, perpendicular to its length. Find the increase in total surface area and explain why the cut lengths are not needed for the increase.
Hint
Count newly exposed faces instead of recalculating every original face.