Question

a = 7 yards
b = 14 yards
c = 13 yards
you only need to enter the final answer value of the shapes area. you do not need to enter the unit label. round to the nearest tenth if necessary.

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter of a triangle \(s=\frac{a + b+ c}{2}\).
Substitute \(a = 7\), \(b = 14\), \(c = 13\) into the formula:
\(s=\frac{7 + 14+ 13}{2}=\frac{34}{2}=17\)

Step2: Use Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\)

Substitute \(s = 17\), \(a = 7\), \(b = 14\), \(c = 13\) into Heron's formula:
\(A=\sqrt{17(17 - 7)(17 - 14)(17 - 13)}=\sqrt{17\times10\times3\times4}=\sqrt{2040}\approx45.2\)

Answer:

\(45.2\)