Question

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 would be the area of his rink if it is triangular shaped with sides of length 29 feet, 30 feet, and 35 feet? round to the nearest square foot.

Explanation:

Step1: Calculate the semi - perimeter

The semi - perimeter \(s=\frac{a + b + c}{2}\), where \(a = 29\), \(b = 30\), \(c = 35\).
\(s=\frac{29+30 + 35}{2}=\frac{94}{2}=47\)

Step2: Use Heron's formula

Heron's formula for the area of a triangle is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute \(s = 47\), \(a = 29\), \(b = 30\), \(c = 35\) into the formula:
\(A=\sqrt{47(47 - 29)(47 - 30)(47 - 35)}\)
\(=\sqrt{47\times18\times17\times12}\)
First, calculate \(47\times18\times17\times12=(47\times18)\times(17\times12)=846\times204 = 172584\)
Then \(A=\sqrt{172584}\approx415.43\)

Answer:

415 square feet