Answer:
326 ft²
Step-by-step explanation:
You want to know the area of the library, which is a composite shape.
Area
The area of a composite shape is found by dividing it into shapes whose areas are easy to find. The area of the shape will be a combination of the areas of the simpler shapes.
The formula for the area of a rectangle is ...
A = LW
Extending the middle horizontal line will divide the figure into two rectangles whose dimensions are given on the figure.
The upper rectangle is 30 ft wide and 5 ft high, so its area is ...
A = (30 ft)(5 ft) = 150 ft²
The lower rectangle is 22 ft wide and 8 ft high, so its area is ...
A = (22 ft)(8 ft) = 176 ft²
The area of the library will be the sum of these two rectangular areas:
library area = 150 ft² +176 ft² = 326 ft²
The library area is 326 square feet.
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Alternate solution
The area could be considered to be a rectangle that is 30 ft wide by 5+8=13 ft high, with a rectangle 30-22=8 ft wide and 8 ft high removed from the lower left corner. The difference in area between the overall rectangle and the removed rectangle is ...
(30 ft)(13 ft) -(8 ft)(8 ft) = 390 ft² -64 ft² = 326 ft²
The method shown above does not require calculating missing dimensions, so is more straightforward.
