K, L, M, N-midpoints of the sides of the square ABCD, AC = 10cm. Find the area KMNL.

1. АС and АD are diagonals. With the sides of a square, they form triangles: ABC, BCD, BDC, ABD.

2. The geometric figure formed by connecting the points K, L, M, N is a square, and its sides are the midlines of the above triangles. Each of them is equal to 1/2 of the length of the AC and BD diagonals:

10: 2 = 5 centimeters.

3. Calculate the area (S) of the square KLMN:

S = 5 x 5 = 25 centimeters².

Answer: The area of a square KMNL is 25 centimeters².

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