Question

One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 1 unit wide. 10 5

Answer 1

The shaded region between rectangles, with a 1-unit wide frame, has an area of 26 square units. (Area of larger rectangle - area of smaller rectangle)

To find the area of the shaded region between the two rectangles, subtract the area of the smaller rectangle from the area of the larger rectangle.

1. Area of Larger Rectangle:

The larger rectangle has a length of 10 and a width of 5. Therefore, the area is
`\(10 * 5 = 50\)` square units.

2. Area of Smaller Rectangle:

The smaller rectangle is formed by reducing the dimensions by 2 units on each side (1 unit on each side for the frame). So, its length becomes
10 - 2 = 8 and the width becomes 5 - 2 = 3. The area is
`\(8 * 3 = 24\)` square units.

3. Shaded Area:

Subtract the area of the smaller rectangle from the area of the larger rectangle:

50 - 24 = 26 square units.

Therefore, the shaded region has an area of 26 square units.