Answer:
[tex]Area = 34.2cm^2[/tex]
Step-by-step explanation:
Let the three sides be a, b and c respectively.
Such that:
[tex]a = 8[/tex]
[tex]b = 9[/tex]
[tex]c= 10[/tex]
Required
Determine the area
This is calculated as:
[tex]Area = \sqrt{s(s-a)(s-b)(s-c)[/tex]
Where
[tex]s = \frac{1}{2}(a + b + c)[/tex]
Substitute values for a, b and c
[tex]s = \frac{1}{2}(8 + 9 + 10)[/tex]
[tex]s = \frac{1}{2}(27)[/tex]
[tex]s = 13.5[/tex]
Substitute values for a, b, c and s in
[tex]Area = \sqrt{s(s-a)(s-b)(s-c)[/tex]
[tex]Area = \sqrt{13.5 * (13.5 - 8)* (13.5 - 9)* (13.5 - 10)[/tex]
[tex]Area = \sqrt{13.5 * 5.5* 4.5* 3.5[/tex]
[tex]Area = \sqrt{1169.4375[/tex]
[tex]Area = 34.2[/tex] -- Approximated
