Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an approximation for pi 314 square meters 1,254 square meters 2,822 square meters 312 square meters

To find the area of the shaded region, we need to calculate the area of the isosceles triangle and then subtract the area of the circle.Step 1: Calculate the area of the isosceles triangle.The formula for the area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\).Since we have an isosceles triangle with a base of 58m and two equal legs, we can find the height by creating two right triangles within the isosceles triangle. The base of each right triangle will be half of the base of the isosceles triangle, which is \(\frac{58m}{2} = 29m\).Using the Pythagorean theorem for one of the right triangles, we have:\(\text{leg}^2 = \text{base}^2 + \text{height}^2\)\(58^2 = 29^2 + \text{height}^2\)\(3364 = 841 + \text{height}^2\)\(\text{height}^2 = 3364 - 841\)\(\text{height}^2 = 2523\)\(\text{height} = \sqrt{2523}\)The height is approximately \(\sqrt{2523} \approx 50.23m\) (since we are looking for an approximate answer).Now, we can calculate the area of the isosceles triangle:\(\text{Area}_{\text{triangle}} = \frac{1}{2} \times 58m \times 50.23m\)\(\text{Area}_{\text{triangle}} \approx \frac{1}{2} \times 58m \times 50.23m\)\(\text{Area}_{\text{triangle}} \approx 29m \times 50.23m\)\(\text{Area}_{\text{triangle}} \approx 1456.67m^2\)Step 2: Calculate the area of the circle.The formula for the area of a circle is \(\pi r^2\), where \(r\) is the radius.The diameter of the circle is 20m, so the radius is \(\frac{20m}{2} = 10m\).Now, we can calculate the area of the circle:\(\text{Area}_{\text{circle}} = \pi \times (10m)^2\)\(\text{Area}_{\text{circle}} = 3.14 \times 100m^2\)\(\text{Area}_{\text{circle}} = 314m^2\)Step 3: Subtract the area of the circle from the area of the triangle to find the area of the shaded region.\(\text{Area}_{\text{shaded}} = \text{Area}_{\text{triangle}} - \text{Area}_{\text{circle}}\)\(\text{Area}_{\text{shaded}} \approx 1456.67m^2 - 314m^2\)\(\text{Area}_{\text{shaded}} \approx 1142.67m^2\)The approximate area of the shaded region is 1142.67 square meters. However, this is not one of the options provided. It seems there might be a mistake in the calculation or in the options given. Let's review the options to see if any rounding or mistake could lead to one of the provided answers:- 314 square meters (This is the area of the circle, not the shaded region.)- 1,254 square meters (This is too high compared to our calculation.)- 2,822 square meters (This is much higher than the area of the triangle itself, so it's not possible.)- 312 square meters (This is close to the area of the circle, but not the shaded region.)None of the provided options match the calculated area of the shaded region. It's possible that there is an error in the provided options or in the calculation. However, based on the information given and using the approximation for \(\pi\), the calculated area of the shaded region is approximately 1142.67 square meters.