One way to find the total area is to first find the area of the new bathroom, which is 22 ft by 12 ft, so its area would be 22*12 = 264 square feet. Then add on the area of the new bedroom which is 22 ft by w ft. The "w" is just a placeholder for a number. The area of the new bedroom is 22*w square feet. In total, the two rooms combine to 264+22w
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With that expression in mind, we can use the distributive property to get the same thing. The largest rectangle has a horizontal width of 22 ft, while the vertical length is 12+w. Let's multiply these two values and use the distributive property
width*length = 22*(12+w) = 22*12+22*w = 264+22w
and we get the same answer as before, which helps check to see if we got the right answer.
