Geometry & anglesMCQ · 2 marks

Mei uses identical trapeziums to build a chain of 3 pieces. Each trapezium has three sides of equal length, and its fourth side is 6 cm longer than each of the equal sides. The pieces are joined end to end, each joint along one of the equal sides, so the chain has a perimeter of 50 cm. Find the perimeter of one trapezium.

Need a hint?

Count how many equal sides disappear at each joint, then subtract them from three full perimeters.

Worked answer

Let each equal side be x cm, so the fourth side is (x + 6) cm.
Perimeter of one trapezium = 3x + (x + 6) = 4x + 6 cm.
Each joint hides two equal sides of length x (one from each piece), and there are 2 joints, so 4x cm is removed in total.
Chain perimeter = 3(4x + 6) − 4x = 50, so 12x + 18 − 4x = 50.
8x = 32, so x = 4.
Perimeter of one trapezium = 4 × 4 + 6 = 22 cm.

Answer: 22 cm

Habit

Pupils often forget that the fourth side is 6 cm longer, or they subtract only one side per joint instead of both sides that meet.

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