Stage 8 - Q1 - 2 marks
Find the trapezium area. Parallel sides are 4 cm and 8 cm; perpendicular height is 3 cm.
Hint
Use the perpendicular height with the correct base measurement.
Stage 8 - Q2 - 2 marks
Find the trapezium area. Parallel sides are 5 cm and 9 cm; perpendicular height is 6 cm.
Hint
Use the perpendicular height with the correct base measurement.
Stage 8 - Q3 - 2 marks
A trapezium has parallel sides 7 cm and 11 cm, and height 5 cm. Find its area.
Hint
Add the parallel sides first.
Stage 8 - Q4 - 2 marks
A trapezium has area 60 cm² and parallel sides 8 cm and 12 cm. Find its height.
Hint
Divide twice the area by the sum of parallel sides.
Stage 8 - Q5 - 3 marks
A trapezium has area 54 cm², height 6 cm and one parallel side 7 cm. Find the other parallel side.
Hint
Find the sum before subtracting the known side.
Stage 8 - Q6 - 3 marks
Two equal trapezia have parallel sides 4 cm and 10 cm and height 5 cm. They form one parallelogram. Find the parallelogram area and explain how it checks one trapezium’s area.
Hint
Use the geometrical derivation of the formula.
Stage 8 - Q7 - 4 marks
A trapezium has parallel sides 6 cm and 14 cm and height 8 cm. A rectangle of area 24 cm² is cut from it. Find the remaining area.
Hint
The cutout area is already given.
Stage 8 - Q8 - 4 marks
A trapezium of height 4 cm has parallel sides x cm and \((x+6)\) cm. Its area is 52 cm². Find both sides.
Hint
The two parallel sides are related, so one unknown is enough.
Stage 8 - Q9 - 5 marks
One parallel side of a trapezium increases by 4 cm and the other decreases by 4 cm. Its height is unchanged and both sides remain positive. Prove that its area is unchanged.
Hint
The formula depends on the sum of the two parallel lengths.
Stage 8 - Q10 - 6 marks
A trapezium has parallel sides in the ratio \(3:5\), perpendicular height 4 cm and area 80 cm². Find both parallel sides and verify the area.
Hint
Use the area formula before the ratio-sharing method.