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Question:

Find the area of the shaded region.

[Image of a rectangle with a semicircle on top]

Solution:

Step 1: Find the area of the rectangle.

The rectangle has a length of 10 units and a width of 8 units. Therefore, the area of the rectangle is:

```
Area of rectangle = Length × Width
= 10 × 8
= 80 square units
```

Step 2: Find the area of the semicircle.

The semicircle has a radius of 5 units. Therefore, the area of the semicircle is:

```
Area of semicircle = (πr²) / 2
= (π × 25) / 2
= 25π / 2 square units
```

Step 3: Subtract the area of the semicircle from the area of the rectangle to find the area of the shaded region.

```
Area of shaded region = Area of rectangle - Area of semicircle
= 80 - 25π / 2
= 80 - 12.5π square units
```

Therefore, the area of the shaded region is approximately 51.84 square units.