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A hexagonal tabletop is cut by a line joining two opposite corners into two identical trapeziums. Each trapezium has parallel sides 20 cm and 40 cm and a height of 17 cm. Find the area of the whole tabletop.

Class 8MensurationMensuration
  • A
  • B
  • C
  • D

Step-by-Step Solution

One trapezium = ½ × = ½ × . The tabletop is two of them: . Trap : stopping after one half. Trap : forgetting the ½ and then doubling. Trap : using only the longer parallel side , which ignores the shorter one.
Answer: D)

Key idea: Area of a trapezium

**Area of a trapezium = ½ × (sum of parallel sides) × height.**

The height is the **perpendicular distance** between the two parallel sides — NOT the slant length of the non-parallel side.

Example: parallel sides 8 cm and 5 cm, height 4 cm. Area = ½ × = ½ × .

Why ½? You can split a trapezium into a rectangle plus a triangle (or chop and rearrange into a rectangle of the average parallel side). The factor of ½ comes from averaging the two parallel sides.

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