Composite 2D Figure - Free Printable

To find the area of the shaded blue region, we need to break the shape down into simpler parts that we know how to calculate.

Step 1: Identify the main shapes
The entire figure looks like a trapezoid (a four-sided shape with one pair of parallel sides) with a semi-circle cut out from the right side.

* The Trapezoid:
* The top base is $50 \text{ cm}$.
* The bottom base is $80 \text{ cm}$.
* To find the height of the trapezoid, look at the semi-circle on the right. The dashed line shows the radius is $20 \text{ cm}$. Since the semi-circle fits perfectly between the top and bottom bases, the diameter of the circle is equal to the height of the trapezoid.
* Diameter = $2 \times \text{radius} = 2 \times 20 \text{ cm} = 40 \text{ cm}$.
* So, the height of the trapezoid is $40 \text{ cm}$.

* The Semi-circle:
* The radius ($r$) is given as $20 \text{ cm}$.
* This part is empty (white), so we will calculate its area and subtract it from the total area.

Step 2: Calculate the area of the full trapezoid
The formula for the area of a trapezoid is:
$$ \text{Area} = \frac{( \text{top base} + \text{bottom base} ) \times \text{height}}{2} $$

Plug in our numbers:
$$ \text{Area}_{\text{trapezoid}} = \frac{( 50 + 80 ) \times 40}{2} $$
$$ \text{Area}_{\text{trapezoid}} = \frac{130 \times 40}{2} $$
$$ \text{Area}_{\text{trapezoid}} = \frac{5200}{2} $$
$$ \text{Area}_{\text{trapezoid}} = 2600 \text{ cm}^2 $$

Step 3: Calculate the area of the semi-circle
The formula for the area of a full circle is $\pi \times r^2$. Since this is half a circle, we divide by 2.
$$ \text{Area}_{\text{semi-circle}} = \frac{\pi \times r^2}{2} $$

Plug in the radius ($20$):
$$ \text{Area}_{\text{semi-circle}} = \frac{\pi \times 20^2}{2} $$
$$ \text{Area}_{\text{semi-circle}} = \frac{\pi \times 400}{2} $$
$$ \text{Area}_{\text{semi-circle}} = 200\pi \text{ cm}^2 $$

Using $\pi \approx 3.14159$:
$$ \text{Area}_{\text{semi-circle}} \approx 200 \times 3.14159 $$
$$ \text{Area}_{\text{semi-circle}} \approx 628.32 \text{ cm}^2 $$

Step 4: Subtract to find the shaded area
Now, subtract the area of the white semi-circle from the area of the whole trapezoid.

$$ \text{Shaded Area} = \text{Area}_{\text{trapezoid}} - \text{Area}_{\text{semi-circle}} $$
$$ \text{Shaded Area} = 2600 - 628.32 $$
$$ \text{Shaded Area} = 1971.68 \text{ cm}^2 $$

*(Note: If you use $\pi \approx 3.14$, the semi-circle area is $628$, and the final answer is $1972$. Both are generally accepted depending on the precision required. I will provide the answer rounded to two decimal places using standard pi value.)*

Final Answer:
1971.68 cm²