Question

in $delta ijk$, $i = 9.2$ inches, $j = 3.7$ inches and $k = 8.3$ inches. find the area of $delta ijk$ to the nearest square inch.

Explanation:

Step1: Calculate semi - perimeter

Let \(s=\frac{i + j + k}{2}\), where \(i = 9.2\), \(j=3.7\), \(k = 8.3\). Then \(s=\frac{9.2+3.7 + 8.3}{2}=\frac{21.2}{2}=10.6\).

Step2: Use Heron's formula

The area \(A=\sqrt{s(s - i)(s - j)(s - k)}\). Substitute \(s = 10.6\), \(i = 9.2\), \(j = 3.7\), \(k = 8.3\) into the formula: \(A=\sqrt{10.6(10.6 - 9.2)(10.6 - 3.7)(10.6 - 8.3)}=\sqrt{10.6\times1.4\times6.9\times2.3}\). First, calculate \(10.6\times1.4\times6.9\times2.3=10.6\times(1.4\times6.9\times2.3)=10.6\times(9.66\times2.3)=10.6\times22.218 = 235.5108\). Then \(A=\sqrt{235.5108}\approx15.346\).

Answer:

15 square inches