Two parallel sides, averaged
A garden has four sides. Two are parallel, 11 and 7 paces long. A pace is the length of one step. The parallel sides are 4 paces apart. What is its area?
- A trapezium: parallel sides 11 and 7, gap 4.
- A diagonal splits it into two triangles.
- Half × 11 × 4 = 22. Half × 7 × 4 = 14.
- 22 + 14 = 36 — the average rule agrees.
Average the parallel sides, then multiply by the gap
The area is 36 square paces.
Trapezium — a four-sided shape with at least one pair of parallel sides.
A diagonal is a line between opposite corners. A diagonal splits the trapezium into two triangles. Both triangles have the same height, the 4-pace gap. Adding them gives ½ × 11 × 4 + ½ × 7 × 4. That is ½ × (11 + 7) × 4. The average of 11 and 7 is 18 ÷ 2 = 9.
Rule: area of a trapezium = ½ × height × (sum of the parallel sides).
For 11 and 7, 4 apart, that is ½ × 18 × 4. Half of 18 is 9, and 9 × 4 = 36. Only the two parallel sides are added.
Slide the top side and the height. Watch the area.
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