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The area of a regular hexagon The bottom surface of this part is hexagonal, with a floor area of 120 square centimeters, a height of 5 centimeters and a volume of () cubic centimeters
Many shapes can be calculated by multiplying land area by height
For example, cube, cylinder, cuboid, etc
This is no exception
Use 120 * 5 = 600
How to calculate the area of regular hexagon?
Draw a circle. At the center of a regular hexagon is the center of the circle, and the sum of the areas of the six regular triangles
How to calculate the area of a regular hexagon?
Know the side leader a
Then the area = 6 ×√ 3 / 4A? 2 = 3 √ 3 / 2A
√ 3 / 4A? Is the area of each equilateral triangle
How to calculate the area of a regular hexagon?
If the radius is r, then the side length of the regular polygon is a = 2R * sin (π / N) 1. Form a triangle from the center of the circle and the two ends of an edge of the regular polygon, the height is h = R * cos (π / N) = a * CTG (π / N) / 2, the area s = a * H / 2 = a ^ 2 * CTG (π / N) / 2
How to calculate the area of a regular hexagon?
If the center of a regular hexagon is connected with six vertices, then the hexagon is divided into six congruent regular triangles, and the side length is the side length of the hexagon. If the side length of a regular hexagon is a, then s regular hexagon = 6 × √ 3a × A / 4 = (3 √ 3A ^ 2) / 2
The calculation of the area of regular hexagon Given that the side length of a regular hexagon is 2, what is its area? (write the calculation process)
It is equal to the area sum of six equilateral triangles with side length 2
Or the area sum of 3 congruent rhombus with side length of 2 and. 3S rhombus
The simplest way is to sum up the area of two congruent isosceles trapezoid [upper bottom is 2, bottom is 4, height is √ 3] and. 2S ladder
S=(2+4)√3=6√3
What is the area of a regular hexagon?
Suppose that the side length is a, along the diagonal line passing through the center, it is divided into two trapezoids with the upper bottom a, the lower bottom being 2a, and the height being two-thirds of the root sign 3a, which is equivalent to a parallelogram with the bottom of 3a and the height of the two-thirds root sign 3a. The area s = 3A * root sign 3A / 2 = three times the root sign 3A * a
over
Area formula of regular hexagon
s=3√3a^2
As shown in the figure, AB is the diameter of ⊙ o, the degree ratio of quadrilateral ABCD connected to ⊙ o, arc BC, arc CD, arc ad is 3:2:4, Mn is the tangent of ⊙ o, C is the tangent point, then the degree of ⊙ BCM is______ Degree
Connect OC,
Then ∠ OCM = 90 °,
∵ the degree ratio of arc BC, arc CD and arc ad is 3:2:4;
set up
If BC = 3x, then
CD=2x，
AD=4x，
A kind of
BC+
CD+
AD=180°，
That is, 3x + 2x + 4x = 180 °,
It is found that x = 20 °, 3x = 60 °, i.e., ∠ BOC = 60 °,
∵OB=OC，
∴∠OBC=∠OCB=1
2（180°-∠BOC）=1
2（180°-60°）=60°，
∠BCM=∠OCM-∠OCB=90°-60°=30°．
As shown in the figure, in the rectangle ABCD, e is the midpoint of BC, and de ⊥ AC, then CD: ad=______ .
As shown in the figure: ∵ ad ∥ BC, e is the midpoint of BC,
∴△ECO∽△DAO，
∵AD=BC，EC=1
2BC
∴EC
AD＝ CO
AO=1
2；
∵ ADC = 90 ° AC ⊥ ed, ∵ CAD is the common angle of △ ADC and △ AOD,
∴△ADC∽△AOD，
Similarly, △ ADC ∽ doc can be obtained,
﹤ ADC ∽ AOD ∽ doc, namely ad
DC＝ AO
OD＝ DO
OC，
∵ it has been proved that CO: Ao = 1:2,
∴OD=
AO•OC=
2, namely CD: ad=
2：2．
So the answer is:
2：2
RELATED INFORMATIONS
- 1. As shown in the figure, in the rectangle ABCD, e is the midpoint of BC, and de ⊥ AC, then CD: ad=______ .
- 2. It is known that the four vertices of the trapezoid ABCD are all on the circle O, ad is parallel to BC, known ad = 12cm, BC = 16cm, the diameter of circle O is 20cm, calculate the area of trapezoid Urgent I don't have a picture. Do you think it is
- 3. As shown in the figure, we know that in ⊙ o, the diameter Mn = 10, the four vertices of square ABCD are on the radius OM, OP and ⊙ o respectively, and ᙽ POM = 45 °, then the length of AB is () A. 5 B. 4 C. 3 D. Five
- 4. 0
- 5. 0
- 6. 0
- 7. As shown in the figure, in RT △ ABC, ∠ C = 90 °, B = 30 °, BC = 4cm, with point C as the center of the circle and 2cm long as the radius as the circle, then the position relationship between ⊙ C and ab is () A. Separation B. Tangency C. Intersection D. Tangency or intersection
- 8. In the triangle ABC, (isosceles triangle), ab = AC, angle BAC = 120 degrees, ad is perpendicular to AC, if the square of AB = 3, then BC The figure is a large isosceles triangle. The large triangle has a small isosceles triangle. A is the vertex. D is a point on BC
- 9. As shown in Figure 1, △ ABC is inscribed in ⊙ o, ad bisects BAC, the intersection line BC is at point E, and the intersection ⊙ o is at point D (1) It is proved that Mn is the tangent line of ⊙ o; (2) The results showed that ab · AC = ad · AE; (3) As shown in Figure 2, AE bisects the outer angle of BAC ∠ fac, the extension line of BC intersects at point E, and the extension line of EA intersects ⊙ o at point D. conclusion whether AB? AC = ad? AE is still valid? If yes, please write the proof process; if not, please explain the reasons
- 10. Ad, AE and CB are all tangent lines, and the tangent points are D, e, F, ad = 4, so we can find the circumference of the triangle ABC
- 11. The triangle whose largest angle is an acute angle must be an acute triangle () in a triangle, at least two angles are acute angles
- 12. Trigonometric function relation of the same acute angle sin^2 x + cos^2 x tan A * cot A
- 13. If cos alpha = 3 / 5, alpha belongs to (- π, 0), then cos (π / 4-alpha)
- 14. Why when n tends to infinity, the limit of one part of n to open an n-th root is one
- 15. What is the sum of the factorials from 0 to positive infinity n
- 16. Is it fifty-five or fifty-four sixty-one?
- 17. If a is not divisible by 2 It is proved that a squared minus 1 can be divisible by 8
- 18. +6! How to calculate, seek specific steps
- 19. Let basketball team a and team B play. There is one winning team in each game. If one team wins four games, the game ends. Assuming that the probability of a and B winning in each game is half, try to find the expectation of the number of matches If X My calculation: P (x = 6) = C (2,5) * (1 / 2) * (1 / 2) * (1 / 2) * (1 / 2) * (1 / 2) * (1 / 2) * (1 / 2) * 2 = 5 / 8), is there any error in this?
- 20. On permutation and combination algorithm From 1 to 93, take any 8 numbers to form a sequence, which should not be in descending order. That is to say, any number in the sequence should be greater than or equal to the number in front of it. How many permutations are there? For example: {1,2,3,4,5,6,7,8} {1,2,2,2,5,6,7,8} {1,2,3,4,5,6,7,93} {10,11,30,40,44,50,60,90} The above arrangements are in line with the requirements Here are a few of the arrangements that do not meet the requirements: {1,2,3,2,4,5,6,7} {10,10,10,9,10,10,10,11} The algorithm of the first floor of hachet I would like to add that I want to express this algorithm in the form of permutation and combination. For example, how many kinds of selection methods can be expressed as three out of ten elements C (10,3), and so on I don't know if I can express this algorithm only by permutation and combination. If not, I'll have to write a cycle. In addition, I just forgot to say that if the answer given above is 1x8x6x0x8x7x8x9x4x3x00 (because continuous numbers are recognized by the system as phone numbers, they are separated by x)~