Question

The dartboard below is composed of a square within a square.

image.png

The inside square has side lengths of 1 inch. The outside square has side lengths of 3 inches.



What is the area of the shaded region?

Answer 1

To find the area of the shaded region on the dartboard, we need to calculate the area of both the outside square and the inside square.

1. **Calculate the area of the outside square:**
The side length of the outside square is 3 inches.
\[
\text{Area of the outside square} = \text{side}^2 = 3^2 = 9 \text{ square inches}
\]

2. **Calculate the area of the inside square:**
The side length of the inside square is 1 inch.
\[
\text{Area of the inside square} = \text{side}^2 = 1^2 = 1 \text{ square inch}
\]

3. **Calculate the area of the shaded region:**
The shaded area is the area of the outside square minus the area of the inside square.
\[
\text{Area of the shaded region} = \text{Area of the outside square} - \text{Area of the inside square}
\]
\[
\text{Area of the shaded region} = 9 - 1 = 8 \text{ square inches}
\]

Thus, the area of the shaded region is \( \boxed{8} \) square inches.