Respuesta :

What you're seeing here is a rectangle attached to a semi-circle.

To find the area of a rectangle, multiply the length times the width. (lw)

To find the area of a semi-circle, use this formula:

[tex] \frac{1}{2} \pi \times {r}^{2} [/tex]

To find your answer, first get the two dimensions of the rectangle

[tex]l = 7 \: w \:= 3[/tex]

and multiply.

[tex]lw = 21[/tex]

Now look at the semi-circle. We can see that it has a diameter of 3. Since the radius is equal to half, 1/2 the diameter, our radius is then 1.5.

[tex] \frac{1}{2} \times \pi \times {1.5}^{2} [/tex]

We can also calculate this manually:

[tex]0.5 \times 3.14 \times 1.5 \times 1.5[/tex]

Add the dimensions of both objects together now.

[tex]21 + 3.5325 = 24.5325 \: cm {}^{2} [/tex]

Your geometric figure has a total area of 24.5325 cm.

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