To find the area of the rectangle LMNO with vertices L(−5,7), M(−1,7), N(−1,−3), and O(−5,−3), we first need to determine the lengths of the sides of the rectangle.
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Length of the base: The distance between points L(−5,7) and M(−1,7) can be calculated using the formula for distance between two points on a horizontal line, which is simply the difference in x-coordinates:
\[ \text{Length} = |x_2 - x_1| = |-1 - (-5)| = |-1 + 5| = |4| = 4 \text{ units} \]
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Length of the height: The distance between points L(−5,7) and O(−5,−3) can be calculated using the formula for distance between two points on a vertical line, which is the difference in y-coordinates:
\[ \text{Height} = |y_2 - y_1| = |−3 - 7| = |−10| = 10 \text{ units} \]
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Area of the rectangle: The area \(A\) of the rectangle is given by the formula:
\[ A = \text{Length} \times \text{Height} = 4 \times 10 = 40 \text{ square units} \]
Therefore, the area of rectangle LMNO is \( \boxed{40} \) square units.