Question

The height of triangle XYZ is the distance from point Y to XZ. Find the area of the triangle. Round your answer to the nearest tenth, if necessary.

Answer 1

Area of the triangle, XYZ = 1/2(XZ)(AY)

Therefore,

`XZ=\sqrt[]{(0+2)^2+(2-6)^2_{}}`
`\begin{gathered} XZ=\sqrt[]{4+16} \\ =\sqrt[]{20} \\ =4.47 \end{gathered}`

Similarly,

`AY=\sqrt[]{(3+1)^2+(6-4)^2}`
`\begin{gathered} AY=\sqrt[]{16+4} \\ =\sqrt[]{20} \\ =4.47 \end{gathered}`

Therefore, the area is,

`\begin{gathered} (1)/(2)* XZ* AY=(1)/(2)*√(20)*\sqrt[]{20} \\ =(1)/(2)*20 \\ =10 \end{gathered}`

So, area of triangle XYZ is 10