Question

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
.

An image shows a right triangle with a circle cut out of it. The legs that make up the right triangle are both 60 meters. The diameter of the circle cut out is 20 meters. All of the triangle is shaded, except where the circle is cut out.

Answer 1

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.