Is this correct?? Please dont mine the little notes I took when solving it..

A= 12, base= 16

Area= (1/2)(12)(16) = 96

384+96 =480

Semi Circle should be something like =(1/2) pir^2

diameter= hypotenuse= sqrt(12^2 +16^2) = 20

radius= r= d/2= 20/2

Semi Circle= (1/2) pi 10^2= 50pi= 157.0796327

Total = 480+157.0796327=637.0796327. Rounding to the nearest hundred would give me 637.08??

Answer and Step-by-step explanation:

Yes, all of your calculations are correct!!

The area of one rectangle is 192, and since there are 2 rectangles, we multiply 192 by 2, which results in 384.

The area of a triangle is [tex]A = \frac{(Height)(Base)}{2}[/tex], which you got to be 96.

The Semi Circle would have half of the area of a circle, so you are correct when you multiply the equation by [tex]\frac{1}{2}[/tex].

To find that diameter, we need to use the Pythagorean Theorem.

[tex]12^{2} + 16^{2} = d^{2} \\\\144 + 256 = d^{2} \\\\400 = d^2\\\\d = 20[/tex]

So the diameter is 20, and the radius is 10 (20 divided by 2 = radius).

Plug that into the equation, and you get the answer to be [tex]50\pi[/tex], or 157.0796327.

157.0796327 + 384 + 96 = 637.08 (rounded to the nearest hundredth).

Good job!

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