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Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood chipped path running through their yard. What wouldbe the area of his rink if it is triangular-shaped with sides of length 18 feet, 20 feet, and 22 feet? Round to the nearest square foot.

Bob wants to build an ice skating rink in his backyard but his wife says he can only use the part beyond the wood chipped path running through their yard What w class=

Respuesta :

In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:

[tex]A=\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}[/tex]

Where p is the semi-perimeter.

So, calculating the value of p and then the area of the triangle, we have:

[tex]\begin{gathered} p=\frac{a+b+c}{2}=\frac{18+20+22}{2}=\frac{60}{2}=30 \\ A=\sqrt{30\left(12\right)\left(10\right)\left(8\right)} \\ A=\sqrt{28800} \\ A=169.7\text{ ft^^b2} \end{gathered}[/tex]

Rounding to the nearest square foot, the area is 170 ft².

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