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.
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Length of XY
Point X = \((x_1,y_1)=(-5,-1)\)
Point Y= \((x_2,y_2)=(-5,-10)\)
\(XY=\sqrt{(-5-(-5))^2+(-10-(-1))^2}\)
\(XY=\sqrt{(0)^2+(-9)^2}\)
\(XY=\sqrt{81}\)
\(XY=9\)
Length of YZ
Point Y= \((x_1,y_1)=(-5,-10)\)
Point Z = \((x_2,y_2)=(-9,-7)\)
\(YZ=\sqrt{(-9-(-5))^2+(-7-(-10))^2}\)
\(XY=\sqrt{(-4)^2+(3)^2}\)
\(YZ=\sqrt{(-4)^2+(3)^2}\)
\(YZ=\sqrt{16+9}\)
\(YZ=\sqrt{25}\)
\(YZ=5\)
Length of XZ
Point X = \((x_1,y_1)=(-5,-1)\)
Point Z = \((x_2,y_2)=(-9,-7)\)
\(XZ=\sqrt{(-9-(-5))^2+(-7-(-1))^2}\)
\(XZ=\sqrt{(-4)^2+(-6)^2}\)
\(XZ=\sqrt{16+36}\)
\(XZ=\sqrt{52}\)
\(XZ=7.2\)
So, to find the area of triangle we will use heron's formula .
\(Area =\sqrt{s(s-a)(s-b)(s-c)}\)
Where \(s=\frac{a+b+c}{2}\)
a,b,c are sides of triangle
a=9
b=5
c=7.2
\(s=\frac{9+5+7.2}{2}\)
\(s=10.6\)
\(Area =\sqrt{10.6(10.6-9-a)(10.6-5)(10.6-7.2)}\)
\(Area =\sqrt{322.9184}\)
\(Area =17.96\)
Hence the area of triangle is 17.96 units squared
