AMC 8 L2: Basic Geometry

Complete problem set with solutions and individual problem pages

Problem 6 Easy

Points A, B, C and D are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square? (2006 AMC8 Problem, Question #05)

  • A.

    15

  • B.

    20

  • C.

    24

  • D.

    30

  • E.

    40

Answer:D

Solution 1: Drawing segements AC and BD, the number of triangles outside square ABCD is the same as the number of triangles inside the square. Thus areas must be equal so the area of ABCD is half the area of the larger square which is \frac{60}{2}=\text{D} 30.

Solution 2: If the side length of the larger square is x, the area of the smaller square is \frac{{{x}^{2}}}{2}.

Thus, the area of the smaller square in the picture is \frac{60}{2}=\text{D} 30.

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