The length of the smaller rectangle is 1/2*40 = <<1/2*40=20>>20 meters.

The width of the smaller rectangle is 1/2*20 = <<1/2*20=10>>10 meters.

Since the area of a rectangle is found by multiplying the length times the width, the total area of the smaller rectangle is 20*10 = <<20*10=200>>200 meters square.

# Answer

200
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A rectangle has a length of 40 meters and a width of 20 meters. A similar smaller rectangle has half the length and width of the big rectangle. What's the area of the smaller rectangle?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
200
A rectangle has a length of 40 meters and a width of 20 meters. A similar smaller rectangle has half the length and width of the big rectangle. What's the area of the smaller rectangle?
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