AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 14 Medium

As shown in the figure, in triangle \triangle ABC, the sides AB and AC are divided into five equal parts by four segments parallel to BC. If the area of \triangle ABC is S, what is the sum of the areas of the shaded regions labeled ② and ④?

  • A.

    \frac{S}{3}

  • B.

    \frac{2S}{5}

  • C.

    \frac{3S}{7}

  • D.

    \frac{5S}{8}

  • E.

    \frac{3S}{5}

Answer:B

From the graph, {{S}_{②}}+{{S}_{④}}=\frac{2S}{5}.

The answer is \text{B}.

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