A square with a side is given.How will the area of the resulting figure change if one side of the square is increased by 1 m and the other is reduced by the same amount.
S sq. = a * a = a² (m²).
After changing the parameters of the side of the square, we get a rectangle shape with sides:
(a + 1) m – length;
(a – 1) m – width.
We find the area of the rectangle by the formula:
S straight. = (a + 1) * (a – 1) = a² – 1 (m²).
S sq. > S straight
a² – (a² – 1) = 1 (m²).
Answer: the area of the resulting rectangle is less than the area of the square by 1 m².
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