Answer:
17.96 units squared
Step-by-step explanation:
Refer the attached figure .
Point X = (−5, −1)
Point Y=(−5, −10)
Point Z=(−9, −7)
In ΔXYZ , to find the length of sides we will use distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of XY
Point X = [tex](x_1,y_1)=(-5,-1)[/tex]
Point Y= [tex](x_2,y_2)=(-5,-10)[/tex]
[tex]XY=\sqrt{(-5-(-5))^2+(-10-(-1))^2}[/tex]
[tex]XY=\sqrt{(0)^2+(-9)^2}[/tex]
[tex]XY=\sqrt{81}[/tex]
[tex]XY=9[/tex]
Length of YZ
Point Y= [tex](x_1,y_1)=(-5,-10)[/tex]
Point Z = [tex](x_2,y_2)=(-9,-7)[/tex]
[tex]YZ=\sqrt{(-9-(-5))^2+(-7-(-10))^2}[/tex]
[tex]XY=\sqrt{(-4)^2+(3)^2}[/tex]
[tex]YZ=\sqrt{(-4)^2+(3)^2}[/tex]
[tex]YZ=\sqrt{16+9}[/tex]
[tex]YZ=\sqrt{25}[/tex]
[tex]YZ=5[/tex]
Length of XZ
Point X = [tex](x_1,y_1)=(-5,-1)[/tex]
Point Z = [tex](x_2,y_2)=(-9,-7)[/tex]
[tex]XZ=\sqrt{(-9-(-5))^2+(-7-(-1))^2}[/tex]
[tex]XZ=\sqrt{(-4)^2+(-6)^2}[/tex]
[tex]XZ=\sqrt{16+36}[/tex]
[tex]XZ=\sqrt{52}[/tex]
[tex]XZ=7.2[/tex]
So, to find the area of triangle we will use heron's formula .
[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s=\frac{a+b+c}{2}[/tex]
a,b,c are sides of triangle
a=9
b=5
c=7.2
[tex]s=\frac{9+5+7.2}{2}[/tex]
[tex]s=10.6[/tex]
[tex]Area =\sqrt{10.6(10.6-9-a)(10.6-5)(10.6-7.2)}[/tex]
[tex]Area =\sqrt{322.9184}[/tex]
[tex]Area =17.96[/tex]
Hence the area of triangle is 17.96 units squared
