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Sacar area de el segmento sombreado. Pi es igual a 3

To find the area of the shaded region between the two semicircles, we can calculate the area of the larger semicircle and subtract the area of the smaller semicircle.

### Step 1: Areas of Semicircles

We know the formula for the area of a semicircle is:

\[
A = \frac{1}{2} \pi r^2
\]

Given that \( \pi = 3 \), the formula simplifies to:

\[
A = \frac{3}{2} r^2
\]

#### Radius of Larger Semicircle:
The larger semicircle \( \overset{\frown}{DA} \) has a radius equal to the distance from \( D \) to \( E \), which is \( 3 + 3 = 6 \) cm.

\[
A_{\text{large}} = \frac{3}{2} \times 6^2 = \frac{3}{2} \times 36 = 54 \, \text{cm}^2
\]

#### Radius of Smaller Semicircle:
The smaller semicircle \( \overset{\frown}{CA} \) has a radius of \( 3 \) cm.

\[
A_{\text{small}} = \frac{3}{2} \times 3^2 = \frac{3}{2} \times 9 = 13.5 \, \text{cm}^2
\]

### Step 2: Shaded Area

Now, we subtract the area of the smaller semicircle from the area of the larger semicircle:

\[
\text{Shaded Area} = A_{\text{large}} - A_{\text{small}} = 54 - 13.5 = 40.5 \, \text{cm}^2
\]

Thus, the area of the shaded region is \( 40.5 \, \text{cm}^2 \).

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Do you want more details on any specific step, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How do we find the area of a quarter circle?
2. What is the formula for the circumference of a semicircle?
3. How do the areas of similar shapes relate to the ratio of their side lengths?
4. Can you compute the area of an annular ring (the region between two concentric circles)?
5. How does the area change if the radii are doubled?

**Tip:** Always ensure that all units are consistent when solving geometry problems.

Learn how to calculate the area of a shaded region between two semicircles using basic geometry. The problem involves finding the areas of the larger and smaller semicircles and subtracting them. Suitable for students in Grades 6-8, with π approximated as 3.

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