In trapezoid ABCD with parallel bases AB and CD, AB = 6 and CD = 14. The diagonals intersect at point E. If the area of triangle ABE is 18, what is the area of trapezoid ABCD?
Answer and explanation
Correct answer: D. 200
- Step 1: Triangles ABE and CDE are similar, with linear ratio k = CD / AB = 14 / 6 = 7/3.
- Step 2: Ratio of areas: Area(CDE) = Area(ABE) k^2 = 18 (7/3)^2 = 18 (49/9) = 2 49 = 98.
- Step 3: For the side triangles: Area(ADE) = Area(BCE) = sqrt(Area(ABE) Area(CDE)) = sqrt(18 98) = sqrt(1764) = 42.
- Step 4: Total area of trapezoid = Area(ABE) + Area(CDE) + 2 * Area(ADE) = 18 + 98 + 42 + 42 = 200.
Answer
200.
Why not the others: 160 computes only (ABE + CDE + 42); 180 is an arbitrary estimate; 240 uses ratio k = 3.
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