Consider a right trapezoidal field. Its two parallel sides are 30 meters and 50 meters long. One of its non-parallel sides, which acts as the height, measures 20 meters. What is the area of this field?

Correct — B. Area of a trapezium = ½ × (sum of parallel sides) × height.

Sum of parallel sides = 30 + 50 = 80 m
Height = the perpendicular side = 20 m
Area = ½ × 80 × 20 = 800 m² → option (b)

Check by splitting: a 30 × 20 rectangle (600 m²) plus a right triangle with legs 20 and 20 (200 m²) = 800 m²

Why the others are wrong

• (a)
  700 square meters — 700 m² = 35 × 20, which takes the mean of the parallel sides as 35 m. The mean of 30 and 50 is 40 m, so the area is 40 × 20 = 800 m².
• (c)
  840 square meters — 840 m² = 42 × 20, a mean width of 42 m. The parallel sides 30 m and 50 m average 40 m, so 840 m² overstates the field by 40 m².
• (d)
  900 square meters — 900 m² = 45 × 20, a mean width of 45 m. The mean of 30 and 50 is exactly 40 m, giving 800 m².

A right trapezium has one non-parallel side perpendicular to both parallel sides, so that side is the height.

Area = ½ × (a + b) × h is the mean of the parallel sides times the distance between them. Here the mean width is (30 + 50) ÷ 2 = 40 m, over a height of 20 m.

The slanted fourth side, √(20² + 20²) = 20√2 ≈ 28.3 m, plays no part in the area.

Key facts

• Area of a trapezium = ½ × (sum of parallel sides) × the perpendicular distance between them.
• In a right trapezium, the side perpendicular to the parallel sides is the height.
• The same area is the mean of the parallel sides × the height: 40 × 20 = 800.

Common traps

• Forgetting the ½ and answering (30 + 50) × 20 = 1600 m².
• Using the slanted side (about 28.3 m) as the height. The height is the side perpendicular to the parallel sides.

No directly related past PYQ was found.