Question

In △XYZ , XZ=9 , YZ=4 , and XY=7 .

Answer 1

Answer:

$A=6\sqrt{5}\ units^2$

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

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where

a, b and c are the length sides of triangle

s is the semi-perimeter of triangle

we have

$a=9\ units,b=4\ units,c=7\ units$

Find the semi-perimeter s  

$s=\frac{9+4+7}{2}=10\ units$

Find the area of triangle

$A=\sqrt{10(10-9)(10-4)(10-7)}$

$A=\sqrt{10(1)(6)(3)}$

$A=\sqrt{180}\ units^2$

Simplify

$A=6\sqrt{5}\ units^2$