Question

question
one rectangle is \framed\ within another. find the area of the shaded region if the \frame\ is 2 units wide.
image of a larger rectangle with a smaller rectangle inside
answer
attempt 1 out of a
units²
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Explanation:

Step1: Find dimensions of inner rectangle

The inner rectangle has length \( l = 6 \) and width \( w = 1 \), so its area \( A_{inner}=l\times w = 6\times1 = 6 \).

Step2: Find dimensions of outer rectangle

The frame is 2 units wide. So, the length of the outer rectangle: \( L = 6 + 2\times2= 10 \) (2 units on each side). The width of the outer rectangle: \( W = 1 + 2\times2 = 5 \) (2 units on each side). Then, the area of the outer rectangle \( A_{outer}=L\times W = 10\times5 = 50 \).

Step3: Find area of shaded region

The shaded area is \( A_{outer}-A_{inner}=50 - 6 = 44 \).

Answer:

44