### Example

Find the area of the shaded region.

#### Solution

The given figure is irregular, but we can break it into two rectangles. The area of the shaded region will be the sum of the areas of both rectangles.

The blue rectangle has a width of 12 and a length of 4. The red rectangle has a width of 2, but its length is not labeled. The right side of the figure is the length of the red rectangle plus the length of the blue rectangle. Since the right side of the blue rectangle is 4 units long, the length of the red rectangle must be 6 units.

The area of the figure is 60 square units.

### Try It

Is there another way to split this figure into two rectangles? Try it, and make sure you get the same area.

### Try It

Find the area of each shaded region:

### Example

Find the area of the shaded region.

#### Solution

We can break this irregular figure into a triangle and rectangle. The area of the figure will be the sum of the areas of triangle and rectangle.

The rectangle has a length of 8 units and a width of 4 units.

We need to find the base and height of the triangle.

Since both sides of the rectangle are 4, the vertical side of the triangle is 3, which is 7−4.

The length of the rectangle is 8, so the base of the triangle will be 3, which is 8−4.

Now we can add the areas to find the area of the irregular figure.

The area of the figure is 36.5 square units.

### Try It

Find the area of each shaded region.

### Example

A high school track is shaped like a rectangle with a semi-circle (half a circle) attached on each end. The rectangle has length 105 meters and width 68 meters. Find the area of the track along with the enclosed area. Round your answer to the nearest hundredth.

#### Solution

We will break the figure into a rectangle and two semi-circles. The area of the figure will be the sum of the areas of the rectangle and the semicircles.

The rectangle has a length of 105 m and a width of 68 m. The semi-circles have a diameter of 68 m, so each has a radius of 34 m.

### Try It

Find the area:

### Try It

Source: Prealgebra. **Provided by**: OpenStax. **License**: *CC BY: Attribution*. **License terms**: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757