Cut a round piece of paper and put it together into an approximate rectangle with the width equal to the radius and the area equal. The circumference of the rectangle is 24.84 cm. It turns out that 24.84 △ 2 = the sum of length and width of 12.42 cm, which is also the sum of half of radius and circumference 12.42 (1 + 3.14) = 3cm, which is the radius Area of circle: 3.14 × 3 & # 178; = 28.26 square centimeter Tell me why

Cut a round piece of paper and put it together into an approximate rectangle with the width equal to the radius and the area equal. The circumference of the rectangle is 24.84 cm. It turns out that 24.84 △ 2 = the sum of length and width of 12.42 cm, which is also the sum of half of radius and circumference 12.42 (1 + 3.14) = 3cm, which is the radius Area of circle: 3.14 × 3 & # 178; = 28.26 square centimeter Tell me why

24.84 △ 2 = the sum of length and width of 12.42 cm, which is also the sum of half of radius and circumference
Perimeter △ 2, get length + width, and the length of the rectangle is half of the circumference of the circle, width is the radius of the circle
12.42 (1 + 3.14) = 3cm, which is the radius
Circumference = π d = 2 π R
And half is: π r = 3.14r
So the sum of length and width is 3.14r + r = 4.14r
4.14 r=12.42
So radius = 12.42 ÷ (3.14 + 1) = 3cm
Area of circle: 3.14 × 3 & # 178; = 28.26 square centimeter