Refer to the above diagram. BD = 6, DX = 9, CX = 24.

Refer to the above diagram. BD = 6, DX = 9, CX = 24.

Give the area of Quadrilateral ABDC.
A. 165
B. 264
C. 90
D. 240
E. 108

Correct Answer: A
Explanation/Reference:
Explanation:


, since both are right; by the Corresponding Angles Theorem,

and Quadrilateral ABDC is a trapezoid.
By the Angle-Angle Similarity Postulate, since

and

(by reflexivity), ΔACX ~ ΔBDX, and since corresponding sides of similar triangles are in proportion,



AC = 16, the larger base of the trapezoid; The smaller base is BD = 6.
CD = CX – DX = 24 – 9 =15, the height of the trapezoid.
The area of the trapezoid is

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