In a trapezium ABCD with AB || CD, the diagonals AC and BD intersect at O. The area of ΔCOD = 8 cm². If AB = 2CD, what is the area of ΔAOB?
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Correct answer: A
Explanation
AB ∥ CD
AC and BD intersect each other at O.
Area of ΔCOD = 8 cm²
AB = 2CD
The ratio of the areas of the triangles formed at the intersection of the diagonals in a trapezium is:
ΔAOB : ΔCOD = AB² : CD²
AB : CD = 2 : 1
ΔAOB : ΔCOD = 2² : 1² = 4 : 1
ΔCOD = 8
ΔAOB = 4 × 8 = 32
Area of ΔAOB = 32 cm²