Solution

Here we have in the rectangle RSTV the side RS = 2 and VT is the hypotenuse of the right triangle VTU where TU = 3 and UV = 4.

By Pythagoras theorem for right triangle we know that

VT = \(\sqrt{3^2 + 4^2}\) =5

So the Area of the shaded region = \(2 * 5\)= 10.
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Notice that that we have a right triangle in the diagram.


You might recognize that 3 and 4 are part of the Pythagorean Triplet 3-4-5, in which case the missing side has length 5


Alternatively, we can apply the Pythagorean Theorem.
If we let x = the length of the hypotenuse of the triangle, we can write: 3² + 4² = x²
Simplify: 9 + 16 = x²
Simplify: 25 = x²
Solve: [b]x = 5[/b]



At this point, we should see that the shaded rectangular region has dimensions 2 by 5

Area of rectangle = (base)(height)
= (2)(5)
= 10

Answer: 10

Cheers,
Brent
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