The length of the sides of the square ABCD is 16 cm. The midpoints of its sides are connected by segments

| April 9, 2021 | education

The length of the sides of the square ABCD is 16 cm. The midpoints of its sides are connected by segments so that they form a square, guess how to calculate the area of this square.

1. The sides of the resulting square at each vertex of the first square formed right-angled isosceles triangles, the legs of which are halves of the sides of the first square, and the hypotenuse of such triangles is side a of the new square.

2. Using the Pythagorean theorem, we find the hypotenuse along two legs.

a ^ 2 = (16: 2) ^ 2 + (16: 2) ^ 2 = 64 + 64 = 128;

a = 128 ^ 1/2 = (16 * 8) ^ 1/2 = 4 * 8 ^ 1/2.

3. As you know, the area of ​​a square is equal to the square of its side.

We calculate the area S of the resulting square.

S = a * a = a ^ 2 = (4 * 8 ^ 1/2) ^ 2 = 16 * 8 = 128 cm ^ 2.

Answer: The area of ​​the resulting square is 128 square centimeters.



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