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Take the three vertices of the equilateral triangle ABC as the center of the circle and 2cm long as the radius, draw three arcs in the triangle, and the total length of the three arcs is cm
The sum of interior angles of triangle is 180 degrees
So you cut out the three fan-shaped parts and put them together to make a semicircle with a radius of 2
So the total length of these three arcs is the length of the semicircle
It's 1 / 2 * 2 * π * 2 = 6.28
As shown in the figure, take the three vertices of the triangle ABC as the center of the circle and 1 as the radius as the circle, and intersect with the triangle into three fan-shaped, and find the perimeter sum of the three shadow sectors
2×3.14×1÷2+6×1
=3.14+6
=9.14，
A: the total perimeter of the three shadow sectors is 9.14
In the triangle ABC, the circle is made by taking three vertices as the center and 1 as the radius respectively, and it is intersected with the triangle into three sectors, and the perimeter sum of the three shadows is calculated
Because the sum of the inner angles of the triangle is 180 °, so the intersection of the triangle into three sectors together is half of the circle. The circumference of the circle is 2 π, so the sum of the circumference of the shadow is π + 6
The figure below is a triangle. Draw an arc with its vertex as the center and radius of 2cm to calculate the shadow area
The sum of the center angles of the three fan shadows is equal to the sum of the interior angles of the triangle: 180 degrees
So the three fans come together to form a semicircle,
That is, the sum of the shadow areas is equal to a semicircle
So s = π * 2 ^ 2 / 2 = 2 π
A triangle, with each vertex as the center of the circle and a radius of 2 cm, draw an arc to find the shadow part
The sum of the interior angles of a triangle is equal to 180 degrees, which is equivalent to a half circle with a radius of 2 cm
Results: 3.14 * 2 ^ 2 / 2 = 6.28
The figure below is a triangle. Take each vertex as the center of the circle and draw an arc with a radius of 4cm to calculate the area of the shadow part
The sum of the center angles of the three fan shadows is equal to the sum of the interior angles of the triangle: 180 degrees
The three fans together form a semicircle,
That is, the sum of the shadow areas is equal to a semicircle
So s = π * 4 ^ 2 / 2 = 8 π cm2
Q: if there is a triangle whose sides are greater than 2cm, draw an arc with 1cm radius to find the area of shadow
Since each side is guaranteed to be greater than 2, that is to say, each circle drawn is separated
Because the sum of the angles in a triangle is 180 degrees, and a circle is 360 degrees
In other words, the three shadow parts add up to be a semicircle
So the area is 1 / 2 * π * 1 * 1 = π / 2
As shown in the figure, the side length of a square is 2. If two relative vertices of the square are taken as the center of the circle, and one side of the square is used as the radius to draw an arc, then the area of the shadow part is______ .
S shadow = 2S sector-s square = 2 × 90 π· 2
360-22=1
2π×22-22=2（π-2）．
So fill in 2 (π - 2)
If the side length of the square is a, and the diagonal vertex is the center of the circle and the side length is the radius, what is the area of the shadow part in the figure?
The drawing method is to draw an arc with a pair of diagonal vertices as the center of the circle and the length of the side as the radius
The area is the sum of the areas of two 1 / 4 circles with radius a minus the area of a square with side length a
2×π×A²/4-A²=πA²/2-A²
A square has a side length of 1, takes 4 vertices as the center of the circle, draws an arc with 1 as the radius, and calculates the area of the figure similar to a square in the middle
It is easy to see that the triangle CDE is equilateral triangle, S1 = square area - equilateral triangle area - 2 Fan areas
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