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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.

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 class=

Sagot :

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

Therefore,

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

Similarly,

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

Therefore, the area is,

[tex]\begin{gathered} \frac{1}{2}\times XZ\times AY=\frac{1}{2}\times\sqrt{20}\times\sqrt[]{20} \\ =\frac{1}{2}\times20 \\ =10 \end{gathered}[/tex]

So, area of triangle XYZ is 10

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