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prestonshelton
Hello!

First you have to find the third side of the triangle using the Pythagorean Theorem

[tex] 4^{2} + 6^{2} = c^{2} [/tex]

Square the numbers

[tex]16 + 36 = c^{2} [/tex]

Add

[tex]52 = c^{2} [/tex]

Take the square root of both numbers

[tex] \sqrt{52} = c[/tex]

Now we know all the numbers we need

To find the lateral area of a triangular prism you use the equation

Al = (a + b + c)h

Al is lateral area
a, b, c are the side lengths of the triangle
h is height

Put in the values we know

[tex]Al = (4 + 6 + \sqrt{52} )8[/tex]

Combine like terms

[tex]Al = (10 + \sqrt{52} )8[/tex]

Simplify the square root

[tex]Al = 8(10 + 2 \sqrt{13} )[/tex]

Al = about 137.689

The answer is [tex]Al = 8(10 + 2 \sqrt{13} )[/tex] or 137.689

Hope this helps!

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