In an isosceles right-angled triangle ABC, angle C = 90 degrees, AB = 5cm. On ray AC, segment CK = AC is plotted, segment CM = BC is plotted on ray BC. Find the area of quadrilateral ABKM.
The ACB triangle is isosceles and rectangular. Then AC = BC, and therefore AC = CK = BC = CM, then AK = BM.
In the quadrilateral ABKM, the diagonals AK and BM are equal and intersect at right angles, then the quadrilateral ABKM is a square. Then Saavkm = AB^2 = 5^2 = 25 cm2.
Answer: The area of the ABKM quadrangle is 25 cm2.
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