2014 AMC 8

Complete problem set with solutions and individual problem pages

Problem 6 Easy

Six rectangles each with a common base width of 2 have lengths of 1, 4, 9, 16, 25, and 36. What is the sum of the areas of the six rectangles?

  • A.

    91

  • B.

    93

  • C.

    162

  • D.

    182

  • E.

    202

Answer:D

Solution 1

The sum of the areas is equal to 2\cdot1+2\cdot4+2\cdot9+2\cdot16+2\cdot25+2\cdot36. This is equal to 2(1+4+9+16+25+36), which is equal to 2\cdot91. This is equal to our final answer of \boxed{\textbf{(D)}~182}.

 

Solution 2

we can just multiply the common width 2 by each of the lengths 1 by 1, the sum would be 182. This is slow and grouping the lengths is easier to. The answer is still \boxed{\textbf{(D)}~182}.

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