Stage 8 - Q1 - 2 marks
A triangular face has base 6 cm and perpendicular face height 5 cm. Find its area.
Hint
Use half base times face height.
Stage 8 - Q2 - 2 marks
A pyramid has four triangular faces of area 15 cm² each. Find their total area.
Hint
Add all four equal faces.
Stage 8 - Q3 - 2 marks
A square pyramid has base side 6 cm and face slant height 5 cm. Find its total surface area.
Hint
Include the square base.
Stage 8 - Q4 - 2 marks
A square pyramid has base side 8 cm and total surface area 160 cm². Find the total area of the four sloping faces.
Hint
Subtract the base area.
Stage 8 - Q5 - 3 marks
A square pyramid has base side 8 cm and total surface area 160 cm². Find its face slant height.
Hint
Separate one triangular face before using its area formula.
Stage 8 - Q6 - 3 marks
A square pyramid roof has base side 10 m and face slant height 7 m. Find the area to cover if the base is not covered.
Hint
A roof covering excludes the horizontal base.
Stage 8 - Q7 - 4 marks
A square pyramid has base side 12 cm, vertical height 8 cm and face slant height 10 cm. A pupil uses 8 cm in the face-area formula. Find the correct surface area and explain the error.
Hint
Locate the triangle whose area you are calculating.
Stage 8 - Q8 - 4 marks
A square pyramid’s base side and face slant height both double. Prove that its surface area becomes four times as large.
Hint
Apply the length change to every term of the formula.
Stage 8 - Q9 - 5 marks
A model pyramid has base side 6 cm and face slant height 5 cm. It needs a 10% allowance for waste when all faces are covered. Find the area of material required.
Hint
Add waste after finding the complete surface area.
Stage 8 - Q10 - 6 marks
Two identical square pyramids, each with base side 8 cm and face slant height 5 cm, are glued base to base. Find the exterior surface area and explain which areas disappear from the separate totals.
Hint
Check your result both by counting exposed faces and by subtracting the glued faces.