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Sample Question 23:
Step 1: The area of a regular octagon is given by the formula , where is the apothem and is the perimeter.
Step 2: This octagon's side length is and the apothem is .
Step 3: The area of the rectangle is given by the formula .
Step 4: From steps 1 and 3, we can observe that the area of the rectangle is half the area of the octagon.
Step 5: Since the area of the octagon is one unit square, the area of the rectangle is unit square.
Therefore, the answer is .
A regular octagon has an area of one square unit. What is the area of the rectangle ?
Answer Keys
Question 23: DSolutions
Question 23Step 1: The area of a regular octagon is given by the formula , where is the apothem and is the perimeter.
Step 2: This octagon's side length is and the apothem is .
Step 3: The area of the rectangle is given by the formula .
Step 4: From steps 1 and 3, we can observe that the area of the rectangle is half the area of the octagon.
Step 5: Since the area of the octagon is one unit square, the area of the rectangle is unit square.
Therefore, the answer is .