AMC 10 Daily Practice Round 4

Complete problem set with solutions and individual problem pages

Problem 18 Easy

In the figure, the area of triangle ABC is 1. Connecting the points that divide segments AB and AC into five equal parts, what is the area of the shaded region in the figure?

  • A.

    \dfrac{13}{25}

  • B.

    \dfrac{3}{5}

  • C.

    \dfrac{16}{25}

  • D.

    \dfrac{18}{25}

  • E.

    \dfrac{4}{5}

Answer:B

The areas of the shaded regions in the figure have a ratio of 1:3:5:7:9 from top to bottom. To find the area of the shaded region, we sum up the areas of the three shaded regions from top to bottom, which correspond to the areas with ratios 1:5:9. Then, we divide this sum by the total sum of all the areas (which corresponds to the total sum of the ratios 1:3:5:7:9 in the figure).

The shaded region's area is \frac{1+5+9}{1+3+5+7+9} = \frac{15}{25} = \frac{3}{5}.

Hence, the area of the shaded region is \boxed{\frac{3}{5}}.

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