Question

one rectangle is \framed\ within another. find the area of the shaded region if the \frame\ is 2 units wide. 10 6

Explanation:

Step1: Calculate outer - rectangle area

The area formula for a rectangle is $A = l\times w$. For the outer rectangle with length $l = 10$ and width $w = 6$, the area $A_{outer}=10\times6 = 60$.

Step2: Calculate inner - rectangle dimensions

Since the frame is 2 units wide on each side, the length of the inner rectangle is $l_{inner}=10 - 2\times2=6$ and the width of the inner rectangle is $w_{inner}=6 - 2\times2 = 2$.

Step3: Calculate inner - rectangle area

Using the area formula for a rectangle, $A_{inner}=l_{inner}\times w_{inner}=6\times2 = 12$.

Step4: Calculate shaded - region area

The area of the shaded region $A = A_{outer}-A_{inner}$. So $A=60 - 12=48$.

Answer:

48