Question

One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide.

the framed one is 5 not op and 3 n the side

Answer 1

To find the area of the shaded region that represents the frame around the inner rectangle, we follow these steps:

1. **Calculate the area of the inner rectangle**: The dimensions of the inner rectangle are given as 5 units (width) and 3 units (height).

\[
\text{Area of inner rectangle} = \text{width} \times \text{height} = 5 \times 3 = 15 \text{ square units}
\]

2. **Determine the dimensions of the outer rectangle**: Since the frame is 2 units wide all around the inner rectangle, we need to add twice the frame width (2 units on each side) to each dimension of the inner rectangle.

- Width of the outer rectangle:
\[
5 + 2 \times 2 = 5 + 4 = 9 \text{ units}
\]

- Height of the outer rectangle:
\[
3 + 2 \times 2 = 3 + 4 = 7 \text{ units}
\]

3. **Calculate the area of the outer rectangle**:
\[
\text{Area of outer rectangle} = \text{width} \times \text{height} = 9 \times 7 = 63 \text{ square units}
\]

4. **Calculate the area of the shaded region (the frame)**: The area of the shaded region can be found by subtracting the area of the inner rectangle from the area of the outer rectangle.
\[
\text{Area of shaded region} = \text{Area of outer rectangle} - \text{Area of inner rectangle} = 63 - 15 = 48 \text{ square units}
\]

Thus, the area of the shaded region is **48 square units**.