Stage 8 - Q1 - 2 marks
Find the parallelogram area. Base is 6 cm and perpendicular height is 4 cm.
Hint
Use the perpendicular height with the correct base measurement.
Stage 8 - Q2 - 2 marks
Find the parallelogram area. Base is 8 cm and perpendicular height is 5 cm.
Hint
Use the perpendicular height with the correct base measurement.
Stage 8 - Q3 - 2 marks
A parallelogram has area 36 cm² and base 9 cm. Find the perpendicular height.
Hint
Reverse the area multiplication.
Stage 8 - Q4 - 2 marks
A parallelogram has base 7 cm, perpendicular height 4 cm and sloping side 5 cm. Find its area.
Hint
Use the measurement perpendicular to the base.
Stage 8 - Q5 - 3 marks
Two parallelograms have the same base 9 cm and perpendicular height 6 cm, but different sloping sides. Compare their areas.
Hint
The area formula does not include a sloping side.
Stage 8 - Q6 - 3 marks
A parallelogram of base 12 cm and height 5 cm has the same area as another with base 10 cm. Find the second height.
Hint
Equal areas provide the connection between the shapes.
Stage 8 - Q7 - 4 marks
A parallelogram has base 14 cm and height 8 cm. Remove a triangle of base 5 cm with the same height. Find the remaining area.
Hint
Calculate the two areas separately before subtraction.
Stage 8 - Q8 - 4 marks
A parallelogram’s base increases from 8 cm to 12 cm while its area stays 72 cm². Find both heights and compare them.
Hint
A larger base requires a smaller height when area is fixed.
Stage 8 - Q9 - 5 marks
A parallelogram’s base doubles and its perpendicular height becomes one third as large. What fraction of its original area remains? Prove your answer.
Hint
Use b and h so the argument works for every parallelogram.
Stage 8 - Q10 - 6 marks
A parallelogram has area 120 cm². Its base and perpendicular height are positive whole numbers adding to 23 cm, with the base longer. Find both dimensions and show that no other factor pair works.
Hint
Use area to restrict the possible integer pairs before using their sum.