Question

One rectangle is "framed" within another. Find the area of the shaded region if the

"frame" is 2 units wide.
5

Answer 1

44 units²

Explanation:

The overall dimensions are the inner rectangle dimensions plus twice the frame width. For a 2-unit frame, the outside dimensions are ...

width = 2 +2(2) = 6 units

height = 5 +2(2) = 9 units

Then the overall area is ...

A = LW = (6 units)(9 units) = 54 units²

The area of the inner rectangle is ...

A = (2 units)(5 units) = 10 unit²

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The area of the frame is the difference between the overall area and the area of the rectangle:

frame area = (rectangle +frame) -(rectangle)

= (54 units²) -(10 units²) = 44 units² . . . . area of frame