AMC 8 Daily Practice Round 7

Complete problem set with solutions and individual problem pages

Problem 7 Easy

As shown in the figure below, the side length of square ABCD is 10 centimeters, and the rectangle EFGH has a length of 8 centimeters and a width of 5 centimeters. What is the difference between the areas of the two shaded parts?

  • A.

    15

  • B.

    20

  • C.

    30

  • D.

    40

  • E.

    60

Answer:E

 

As shown in the figure, let the areas of the three regions be denoted as Ⅰ, Ⅱ, and Ⅲ respectively.

We have:

Ⅰ = \text{Area of square } ABCD - Ⅱ

Ⅲ = \text{Area of rectangle } EFGH - Ⅱ

Then, the difference between the areas of the two shaded parts is: Ⅰ - Ⅲ = \left( \text{Area of square } ABCD - Ⅱ \right) - \left( \text{Area of rectangle } EFGH - Ⅱ \right) = \text{Area of square } ABCD - \text{Area of rectangle } EFGH = 10 \times 10 - 8 \times 5 = 100 - 40 = 60

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