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Find the approximate area of the shaded region belowe, consisting of a right triangle with a circle cut out of it

To find the approximate area of the shaded region, we need to determine the area of the right triangle and then subtract the area of the circle that is cut out of it.

### Step-by-Step Solution

1. **Area of the Right Triangle:**
   The formula for the area of a right triangle is:
   \[
   \text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   Given:
   - Base = 90 m
   - Height = 90 m

   So, the area of the triangle is:
   \[
   \text{Area of the triangle} = \frac{1}{2} \times 90 \times 90 = \frac{1}{2} \times 8100 = 4050 \text{ square meters}
   \]

2. **Area of the Circle:**
   The formula for the area of a circle is:
   \[
   \text{Area of the circle} = \pi \times r^2
   \]
   Given:
   - Diameter of the circle = 40 m
   - Radius \( r \) = \frac{40}{2} = 20 m

   So, the area of the circle is:
   \[
   \text{Area of the circle} = \pi \times 20^2 = \pi \times 400 \approx 3.14 \times 400 = 1256 \text{ square meters}
   \]

3. **Shaded Region:**
   To find the area of the shaded region, subtract the area of the circle from the area of the triangle:
   \[
   \text{Area of the shaded region} = \text{Area of the triangle} - \text{Area of the circle} = 4050 - 1256 = 2794 \text{ square meters}
   \]

### Summary

- **Area of the shaded region:** 2794 square meters

Would you like more details or have any questions?

Here are 5 more questions you can ask:
1. How do you find the area of a trapezoid?
2. Can you explain how to find the circumference of a circle?
3. How do you solve systems of linear equations?
4. What is the area formula for a parallelogram?
5. How do you calculate the volume of a cylinder?

**Tip:** Always double-check the units and ensure consistency throughout your calculations to avoid errors.

Discover how to find the approximate area of a shaded region composed of a right triangle with a circle cut out of it. Step-by-step solution includes calculating the area of the triangle and subtracting the area of the circle. Suitable for Grades 7-9.

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