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 the semi - perimeter

The semi - perimeter $s$ of a triangle with side lengths $i$, $j$, and $k$ is given by $s=\frac{i + j + k}{2}$.
$s=\frac{9.2+3.7 + 8.3}{2}=\frac{21.2}{2}=10.6$ inches.

Step2: Use Heron's formula

Heron's formula for the area $A$ of a triangle is $A=\sqrt{s(s - i)(s - j)(s - k)}$.
$A=\sqrt{10.6(10.6 - 9.2)(10.6 - 3.7)(10.6 - 8.3)}$
$A=\sqrt{10.6\times1.4\times6.9\times2.3}$
$A=\sqrt{10.6\times(1.4\times6.9\times2.3)}$
$A=\sqrt{10.6\times(9.66\times2.3)}$
$A=\sqrt{10.6\times22.218}$
$A=\sqrt{235.5108}\approx15$ square inches.

Answer:

15 square inches