Answer:
area = 6[tex]\sqrt{14}[/tex] units²
Step-by-step explanation:
Given the 3 sides of a triangle, we can use Hero's formula to calculate the area (A)
A = [tex]\sqrt{s(s-a)(s-b(s-c)}[/tex]
where s s the semi perimeter and a, b , c the sides of the triangle
let a = 5, b = 9 and c = 10
s = [tex]\frac{a+b+c}{2}[/tex] = [tex]\frac{5+9+10}{2}[/tex] = [tex]\frac{24}{2}[/tex] = 12
A = [tex]\sqrt{12(12-5)(12-9)(12-10)}[/tex]
= [tex]\sqrt{12(7)(3)(2)}[/tex]
= [tex]\sqrt{504}[/tex]
= [tex]\sqrt{36(14)}[/tex]
= 6[tex]\sqrt{14}[/tex] units²
