To determine the surface area of the puzzle game, we need to calculate the area of each individual piece and then sum them up.
Let's start with the square piece in the center:
This square has sides of length 1 inch, so the area is 1 inch * 1 inch = 1 square inch.
Next, we move to the rectangular pieces:
The top rectangular piece has dimensions of 1 inch by 2 inches, so the area is 1 inch * 2 inches = 2 square inches.
Similarly, the bottom rectangular piece also has dimensions of 1 inch by 2 inches, so the area is 1 inch * 2 inches = 2 square inches.
Finally, we have the triangular pieces:
Each triangular piece is a right triangle with legs of length 1 inch and a hypotenuse of length √2 inches.
The formula to calculate the area of a right triangle is A = (1/2) * base * height.
In this case, the base and height are both 1 inch, so the area is (1/2) * 1 inch * 1 inch = 1/2 square inch.
Now, we sum up the areas of all the pieces:
1 square inch (square piece in the center) + 2 square inches (top rectangular piece) + 2 square inches (bottom rectangular piece) + 1/2 square inch (each triangular piece) = 6.5 square inches.
Therefore, the surface area of this puzzle game is 6.5 square inches.
Use the image to answer the question given that each square is 1 inch find the surface area of this puzzle game
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