Answer:
75 square feet
Explanation:
The original dimensions are 10 ft by 12 ft, so the area is ...
(10 f)(12 ft) = 120 ft^2
The new dimensions are 13 ft by 15 ft, so the area is ...
(13 ft)(15 ft) = 195 ft^2
The difference in area between the original and new play spaces is ...
new area - original area = 195 ft^2 - 120 ft^2 = 75 ft^2
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There are some other ways you can figure this.
1) 3 ft added to the 10 ft side adds an area of (3 ft)(10 ft) = 30 ft^2
3 ft added to the 12 ft side adds an area of (3 ft)(12 ft) = 36 ft^2
The corner area added is a square 3 ft on a side, so is (3 ft)^2 = 9 ft^2
The total of these area additions is ...
(30 +36 +9) ft^2 = 75 ft^2
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2) Adding a 3-ft wide area along both sides and the corner makes a "path" whose width is 3 ft and whose centerline length is 11.5 ft + 13.5 ft = 25 ft. Then the area of that "path" is (3 ft)(25 ft) = 75 ft^2.