Question

find the area of △wxy. write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Calculate semi - perimeter

Let \(a = 37\), \(b = 38\), \(c = 41\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{37+38 + 41}{2}=\frac{116}{2}=58\) ft.

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}\). Substitute \(s = 58\), \(a = 37\), \(b = 38\), \(c = 41\) into the formula: \(A=\sqrt{58(58 - 37)(58 - 38)(58 - 41)}=\sqrt{58\times21\times20\times17}\).
First, calculate \(58\times21\times20\times17=(60 - 2)\times21\times20\times17=(1260-42)\times20\times17 = 1218\times20\times17=24360\times17 = 414120\).
Then \(A=\sqrt{414120}\approx643.5\) \(ft^{2}\).

Answer:

\(643.5\)