To find the approximate area of the shaded region consisting of a right triangle with a circle cut out of it, we first need to calculate the area of the triangle and then subtract the area of the circle.
Step 1: Calculate the area of the right triangle
The formula for the area of a right triangle is:
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, both the base and the height are 60 meters:
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 60 \times 60 = \frac{1}{2} \times 3600 = 1800 \text{ square meters} \]
Step 2: Calculate the area of the circle
The formula for the area of a circle is:
\[ \text{Area}_{\text{circle}} = \pi r^2 \]
First, we need to find the radius of the circle. The diameter of the circle is given as 20 meters, so the radius \( r \) is:
\[ r = \frac{\text{Diameter}}{2} = \frac{20}{2} = 10 \text{ meters} \]
Now, we can calculate the area of the circle:
\[ \text{Area}_{\text{circle}} = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square meters} \]
Step 3: Calculate the area of the shaded region
Now we subtract the area of the circle from the area of the triangle to find the area of the shaded region:
\[ \text{Area}{\text{shaded}} = \text{Area}{\text{triangle}} - \text{Area}_{\text{circle}} \]
\[ \text{Area}_{\text{shaded}} = 1800 - 314 = 1486 \text{ square meters} \]
Final Answer
The approximate area of the shaded region is \( 1486 \) square meters.
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