Given:
The objective is to find the area of triangle ABC and XYZ.
Explanation:
The general formula to find the area of a triangle is,
[tex]A=\frac{1}{2}\times b\times h\text{ . . . . .(1)}[/tex]
To find the area of triangle ABC:
The height of the triangle DC can be calculated using the Pythagorean theorem of triangle ADC.
[tex]DC=\sqrt[]{AC^2-AD^2}\ldots.\text{ .(2)}[/tex]
On plugging the given values in equation (2),
[tex]\begin{gathered} D\C=\sqrt[]{13^3-5^2} \\ =\sqrt[]{169-25} \\ =\sqrt[]{144} \\ =12 \end{gathered}[/tex]
Thus, the height of triangle ABC is 12.
Since it is given in the figure that AD = DB = 5.
So the base of the triangle AB = 5 + 5 = 10.
Now, substitute the obtained values in equation (1).
[tex]\begin{gathered} A(\text{ABC)}=\frac{1}{2}\times AB\times DC \\ =\frac{1}{2}\times10\times12 \\ =60 \end{gathered}[/tex]
To find the area of triangle XYZ:
Since it is given in the figure that XW= WY = 15.
So the base of the triangle XY = 15 + 15 = 30.
The height of the triangle is WZ = 36.
Now, substitute the obtained values in equation (1).
[tex]\begin{gathered} A(XYZ)=\frac{1}{2}\times XY\times WZ \\ =\frac{1}{2}\times30\times36 \\ =540 \end{gathered}[/tex]
Hence, the area of triangle ABC is 60 square units and the area of triangle XYZ is 540 square units.
