It is known that the length of the three sides of a Pentagon is 3cm, 5cm and 2cm, and the four angles are respectively 90 degrees, 90 degrees, 90 degrees and 135 degrees

It is known that the length of the three sides of a Pentagon is 3cm, 5cm and 2cm, and the four angles are respectively 90 degrees, 90 degrees, 90 degrees and 135 degrees

The four angles are 90 degrees, 90 degrees, 90 degrees and 135 degrees. The fifth angle should also be 135 degrees. It can be seen that the Pentagon is formed by cutting off an isosceles right triangle from a rectangle. The length of the rectangle is 5cm and the width is 3cm. The waist of the cut isosceles right triangle is 3-2 = 1cm

How to calculate the area of a Pentagon with a side length of 6 cm

Divide it into an isosceles trapezoid and an isosceles triangle, and then calculate them separately

There are two squares, one side length is 2 cm, the other side length is 6 cm. Can their area ratio and side length ratio form a proportion

Area ratio: 2 * 2:6 * 6 = 4:36 = 1 / 9
Side length ratio: 2:6 = 1 / 3
1 / 9 is not equal to 1 / 3, so it cannot be proportional

As shown in the figure, a straight line L ‖ CD is made through the vertex a of the regular pentagon ABCDE, then ∠ 1=______ .

∵ the polygon ABCDE is a regular pentagon,
∴∠BAE=180°×(5−2)
5=108°，∠ABE=∠AEB，
And ∵ 2 = ∠ Abe,  1 = ∠ AEB,
∴∠1=∠2=1
2（180°-∠BAE），
That is, 2 ∠ 1 = 180 ° - 108 °,
∴∠1=36°．
So the answer is 36 degrees

As shown in the figure, the Pentagon ABCDE is a regular pentagon, and the curve efghij It is called "involute of regular pentagon ABCDE", where EF, FG, GH, hi, ij If AB = 1, then the length of the curve efghij is______ (results retain π)

The center angle of the circle can be calculated by the formula of the inner angle of the polygon, which is 72 degrees,
So the sum of the five arc lengths is 72 π (1 + 2 + 3 + 4 + 5)
180=6π．

As shown in the figure, angle 1, angle 2, angle 3 and angle 4 are the four outer angles of the Pentagon ABCDE. If angle a = 120 degrees, what is the angle | + angle 2 + angle 3 + angle 4?

From the meaning of the title, ∠ 5 = 180 ° - ∠ EAB = 60 °,
And ∵ the sum of the outer angles of the polygon is 360 degrees,
∴∠1+∠2+∠3+∠4=360°-∠5=300°．
So the answer is: 300 degrees
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As shown in the figure, the inner angles of the Pentagon ABCDE are all equal, and ∠ 1 = ∠ 2, ∠ 3 = ∠ 4, find X

 ABCDE is a Pentagon  the sum of the inner angles is 180 × (5-2) = 540 ? e = ∠ C = ∠ EAB = ∠ ABC = ∠ CDE  e = ∠ C = ∠ EAB = ∠ ABC = ∠ CDE = 540 ﹤ 5 = 108  1 + ﹤ 2 = 180 ° - ∵ E = 72 ° 1 =  2 = 36 degrees

Please analyze, as shown in the figure, in the Pentagon ABCDE, ∠ BAE = 120 °... Is as follows As shown in the figure, in the Pentagon ABCDE, ∠ BAE = 120 ° and ∠ B = ∠ e = 90 ° AB = BC, AE = De, find a point m, N on BC and de respectively, so that the circumference of △ amn is the smallest, then the degree of ∠ amn + ∠ anm is () A.100° B.110° C.120° D.130°

∠AMN+∠ANM=120°
Extend AB to a 'so that Ba' = AB,
Extend AE to a "to make AE = EA",
Connect a'm, a ''n
Δ AA'm; ab = Ba '; MB ⊥ AA';
Therefore, MB is a vertical bisector
Am = a'm, similarly, a''n = an
The broken line a'm, nm, a ″ n is the perimeter of △ amn
According to the shortest line between two points, m, n points are on the line a'a '
Now there are
Angle ma'a = ∠ MAA ';
In the same way, NE is the vertical bisector of AA ';
∠NAA''=∠NA’‘A；
And ∠ a'aa '= 120 °;
So ∠ AA 'a' ='aa ''a = 30 °;
The two angles obtained are: amn + anm = 2 ∠ a '+ 2 ∠ a ″ = 2 (180 - ∠ BAE) = 120 °

Draw three circles with the three vertices of a triangle as the center and 2.2 cm as the diameter. What is the sum of the areas of the triangle in the three circles?

1.1×1.1×3.14÷2

A triangle with its three vertices as the center, draw a radius of 2 cm of three circles to find the shadow area?

If the shadow is the overlap of a circle and a triangle
The area is 1 / 2 × π R 2 = 2 π