The sides of the rectangle are equal to 1 cm and 3 cm, all bisectors are drawn
| July 24, 2021 | education
The sides of the rectangle are equal to 1 cm and 3 cm, all bisectors are drawn in it until they intersect. find the area of the quadrangle formed by them.
The bisectors of the corners of the rectangle intersect at points O, H, P, M.
The bisectors of the corners of a rectangle are the diagonals of squares with a side of 1 x 1 cm.
Since the diagonals of the squares intersect at an angle of 90, the HOM and HPM angles are 90.
In the OHPM quadrangle, two corners of straight lines and all sides are equal, then OHPM is a square, and its side is equal to the diagonal of a square with a side of 1 cm.
OH = √2 cm.
Then the area of the ОНРМ is equal to: S = (√2) 2 = 2 cm2.
Answer: The area of the figure is 2 cm2.
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