2001 AMC 8 Problem 11

Attempt Problem 11 of the 2001 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 8 solutions, or check the answer key.

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11.

Points A,A, B,B, CC and DD have these coordinates: A(3,2),A(3,2), B(3,−2),B(3,-2), C(−3,−2)C(-3,-2) and D(−3,0).D(-3,0). What is the area of quadrilateral ABCD?ABCD?
1212
1515
1818
2121
2424
Answer: C
Concepts:coordinate geometrytrapezoidarea
Small hint:
View ABCDABCD as a trapezoid
Big hint:
The parallel vertical sides have lengths 44 and 22
Solution:
We can see that ABCDABCD is a trapezoid since DC‾∥AB‾.\overline{DC} \parallel \overline{AB}.
Recall that the formula for the area of a trapezoid is A=12(b1+b2)h. A = \dfrac{1}{2} (b_1 + b_2) h.
Plugging in b1=DC=2, b_1 = DC = 2, b2=AB=4, b_2 = AB = 4, and h=CB=6, h = CB = 6, we get that A=12(2+4)⋅6 A = \dfrac{1}{2} (2 + 4) \cdot 6 =12⋅6⋅6=18.= \dfrac{1}{2} \cdot 6 \cdot 6 = 18.
Thus, C is the correct answer.
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