Answer :
Answer:
[tex]A=6\sqrt{5}\ units^2[/tex]
Step-by-step explanation:
we know that
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
so
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where
a, b and c are the length sides of triangle
s is the semi-perimeter of triangle
we have
[tex]a=9\ units,b=4\ units,c=7\ units[/tex]
Find the semi-perimeter s
[tex]s=\frac{9+4+7}{2}=10\ units[/tex]
Find the area of triangle
[tex]A=\sqrt{10(10-9)(10-4)(10-7)}[/tex]
[tex]A=\sqrt{10(1)(6)(3)}[/tex]
[tex]A=\sqrt{180}\ units^2[/tex]
Simplify
[tex]A=6\sqrt{5}\ units^2[/tex]
The area of the triangle should be [tex]\sqrt[6]{5} units^2[/tex]
Calculation of the area of the triangle:
Since In △XYZ , XZ=9 , YZ=4 , and XY=7 .
So here heron formula should be applied
[tex]A = \sqrt{s(s -a) (s-b)(s-c)}[/tex]
Here
a, b and c are the length sides of triangle
s is the semi-perimeter of the triangle
The semi-perimeter should be [tex]= (9 + 4 + 7)\div 2 = 10[/tex]
So, the area of the triangle should be
[tex]= \sqrt{10(10-9)(10-4)(10-7)}\\\\= \sqrt{10(1)(6)(3)} \\\\= \sqrt{180}[/tex]
So,
[tex]\sqrt[6]{5} units^2[/tex]
Hence, The area of the triangle should be [tex]\sqrt[6]{5} units^2[/tex]
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