Stage 8 - Q1 - 2 marks
Find the parallelogram area. Base is 9 cm and perpendicular height is 4 cm.
Hint
Use the perpendicular height with the correct base measurement.
Stage 8 - Q2 - 2 marks
Find the trapezium area. Parallel sides are 3 cm and 7 cm; perpendicular height is 5 cm.
Hint
Use the perpendicular height with the correct base measurement.
Stage 8 - Q3 - 2 marks
A triangular prism has cross-sectional area 18 cm² and length 7 cm. Find its volume.
Hint
Area times length gives volume.
Stage 8 - Q4 - 2 marks
Using \(5\text{ miles}\approx8\text{ km}\), convert 22.5 miles to km.
Hint
Use the given approximate conversion.
Stage 8 - Q5 - 3 marks
A trapezium has area 72 cm² and parallel sides 8 and 16 cm. A parallelogram with base 12 cm has the same area. Compare their heights.
Hint
The average of the trapezium’s parallel sides equals the parallelogram base.
Stage 8 - Q6 - 3 marks
A triangular prism has cross-section base 10 cm and height 6 cm, and length 8 cm. Is 240 cm² an appropriate answer for its volume? Correct it.
Hint
Check both the number and the dimension of the unit.
Stage 8 - Q7 - 4 marks
A square pyramid has base side 6 cm and face height 5 cm. A cube has side 4 cm. Compare their total surface areas.
Hint
Equal surface areas need not mean equal shapes or volumes.
Stage 8 - Q8 - 4 marks
Two triangular prisms have equal volume. The first cross-section area is 12 cm² and length 15 cm. The second cross-section area is 20 cm². Find its length.
Hint
Use equal volume to connect the two solids.
Stage 8 - Q9 - 5 marks
A solid triangular prism has right-triangle sides 3, 4 and 5 cm and length 10 cm. A pupil claims its surface area and volume are both 60. Find both and identify the likely confusion.
Hint
A single solid can require different calculations for filling and covering.
Stage 8 - Q10 - 6 marks
A right triangular prism has cross-section sides 6, 8 and 10 cm. Its volume is 288 cm³. It rests on the rectangular face built along the 8 cm side. Find the area of all other faces.
Hint
Recover the missing length before calculating face areas.