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 21 feet, 27 feet, and 28 feet? round to the nearest square foot.

Explanation:

Step1: Calculate the semi - perimeter

The semi - perimeter \(s=\frac{a + b + c}{2}\), where \(a = 21\), \(b = 27\), \(c = 28\).
\(s=\frac{21+27 + 28}{2}=\frac{76}{2}=38\)

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 \(s = 38\), \(a = 21\), \(b = 27\), \(c = 28\) into the formula:
\(A=\sqrt{38(38 - 21)(38 - 27)(38 - 28)}\)
\(=\sqrt{38\times17\times11\times10}\)
\(=\sqrt{38\times17\times110}\)
\(=\sqrt{70460}\approx265.44\)

Answer:

\(265\) square feet