The paper of the square whose length of a diagonal line is 20 cm is placed on the desk.
This paper is rotated on the desk by 45 degrees centering on the one vertex.
Find the area of the portion which this paper passes.
Pi is assumed to be 3.14.
This paper is rotated on the desk by 45 degrees centering on the one vertex.
Find the area of the portion which this paper passes.
Pi is assumed to be 3.14.
Answer
357 cm2
Solution
When rotating 45 degrees of squares ABCD centering on the vertex C, as shown in a figure, a square ABCD moves to A'B'CD'.
The portion which a square passes is the sum total of red and blue portion.
The area of red portion is the same as the area of a square ABCD, it is (20cm × 20cm) / 2 = 200 cm2.
The area of red portion is the same as the area of a square ABCD, it is (20cm × 20cm) / 2 = 200 cm2.
The area of blue portion is a sector with 20 cm in radius and 45 degrees of central angles, it is 20cm × 20cm × 3.14 × 45/360 = 157 cm2.
The area to be found is 200 + 157 = 357 cm2.
