AMC 8 Daily Practice - Area Tricks

Complete problem set with solutions and individual problem pages

Problem 1 Easy

The area of quadrilateral ABCD is 25. It is known that AD = DC, DE = BE, and AE = 2. What is the area of the shaded part?

  • A.

    15

  • B.

    18

  • C.

    19

  • D.

    20

  • E.

    22

Answer:D

 

Since AE = CD, as shown in the figure, draw a line DF through point D perpendicular to the extension of BC at point F.

It can be obtained that \triangle ADE \cong \triangle CDF (congruent triangles).

Therefore, quadrilateral ABCD can be transformed into square DFBE.

The area of square DFBE is 25, so DE = EB = 5.

Then, BC = BF - CF = BF - AE = 5 - 2 = 3.

Thus, the area of the shaded part is: \frac{5 \times (5 + 3)}{2} = 20

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