# Thread: Ratios of Areas Help

1. ## 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!

2. Originally Posted by dvh9
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 $\displaystyle A = \frac{1}{2}bh$. In the first triangle, the base is 3 and the area is 12:

\displaystyle \begin{aligned} 12 &= \frac{1}{2}(3)h \\ h &= 8 \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:

\displaystyle \begin{aligned} A &= \frac{1}{2}(9)(24) \\ &= 108 \end{aligned}

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