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Math Help - Ratios of Areas Help

  1. #1
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    Ratios of Areas Help

    Hello, I have two word problems that I cannot figure out. I've provided the answers from the answer key.

    1) A hexagon with sides 5cm, 6cm, 7cm, 8cm, 9cm, and 10cm has area 123cm^2. If a similar hexagon has longest side of 40 cm, what is its area? (Answer = 1968 cm^2)

    2) Two similar triangles have corresponding sides with lengths 3 and 9. If the area of the first triangle is 12, what is the area of the second triangle? (Answer = 108)


    Any help is appreciated!
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  2. #2
    Super Member
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    Quote Originally Posted by dvh9 View Post
    2) Two similar triangles have corresponding sides with lengths 3 and 9. If the area of the first triangle is 12, what is the area of the second triangle? (Answer = 108)
    The area of a triangle is A = \frac{1}{2}bh. In the first triangle, the base is 3 and the area is 12:

    \begin{aligned}<br />
12 &= \frac{1}{2}(3)h \\<br />
h &= 8<br />
\end{aligned}

    The base of the 2nd triangle is triple the base of the first (3 x 3 = 9), so we triple the height as well (8 x 3 = 24) and find the area:

    \begin{aligned}<br />
A &= \frac{1}{2}(9)(24) \\<br />
&= 108<br />
\end{aligned}


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