How to calculate the net area of irregular figure

General irregular graphics will tell all or part of the side length, part of the angle
Generally, the calculation area is divided into various regular graphs, or some auxiliary lines are added to calculate. Some of them need to use trigonometric function. There are different solutions for different problems. Some problems become very simple by dividing and adding auxiliary lines

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1. It is known that F 1 and F 2 are the focal points of the ellipse x 29 + y 25 = 1, the point P is on the ellipse and ∠ f 1pf 2 = π 3
2. Find the equation of the circle with n (1,3) as the center and tangent to the line 3x-4y-7 = 0
3. 1. The arc length of the sector is a, the radius is r, the sector area is 2, and the concentric angle of the sector is 150 degrees. Then the area of the sector is equal to the area of the circle where the sector is located 3. If the radius of circle O is 4cm and one of the arcs is 2cm long, what is the central angle of the arc
4. The sum of the side length of a square and the width of a rectangle is 20 cm, the perimeter of a square is one and one third of the perimeter of a rectangle, and the width of a rectangle is 4 / 5 of the length. How much is the area of the square and rectangle and the fact How much is the area sum of square and rectangle?
5. 1 ,3,1 ,4 ,9,1 ,8,( ) A 18 B 27 C 36 D12
6. Observe carefully, find out the rule, and then fill in the number 111111111 △ 9 = 123456789 222222222 △ 18= Observe carefully, find out the law, and then fill in the number 111111111÷9=123456789 222222222÷18=123456789 333333333÷27=123456789 （）÷36=123456789 777777777÷（）=（）（）÷（）=（）
7. According to 123456789 * 9 = 1111111101, make the following formula answer 123456789*18=?123456789*36=?123456789*54=?123456789*72=? 123456789*27=?123456789*45=?123456789*63=?123456789*81=?
8. 1 + 0 * 9 = 1,2 + 1 * 9 = 11,3 + 12 * 9 = 111 until 9 + 123456789 * 9 = 111111111 is there any rule
9. Use 9 numbers 123456789 to write three equal fractions. Each number can only be used once
10. Write three fractions of equal size with nine numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. (each number can only be used once). For example: 36 = 714 = 2958
11. It is known that the quadratic function y is equal to the square of x minus 2x plus 4. If there is only one intersection point between the line passing through the origin and the quadratic function, how many such lines are there What I want to ask is: why does this line have no intersection with the parabola when it happens to be the x-axis and y = 0?
12. If the sum of quadratic coefficient and constant term in the quadratic equation AX2 + BX + C = 0 is equal to the coefficient of the first term, then one root of the equation must be () A. 0B. 1C. -1D. ±1
13. Let the right focus of hyperbola C: x24 − y2 = 1 be f and the line L pass through the point F. if the line L intersects both the left and right branches of hyperbola C, then the slope k of line L is () A. K ≤ − 12 or K ≥ 12b. K ＜ − 12 or K ＞ 12C. − 12 ＜ K ＜ 12D. − 12 ≤ K ≤ 12
14. (1 / 2) solving the system of linear equations with three variables {A-B + C = 0 4A + 2B + C = 3 2)
15. The solution of the equations XY + x = 16 and xy-y = 8
16. Given that the function f (x) = (MX ^ 2 + 8x + n) / (x ^ 2 + 1) has a range of [1,9], X ∈ R, find the value of M and N?
17. The function f (x) holds for all real numbers x and y, f (x + y) - f (y) = (x + 2Y + 1) x, and f (1) = 0, (1) find the value of F (0); (2) when 0 ≤ x ≤ 12, f (x) + 3 ＜ 2x + a holds, find the value range of real number a
18. If the vector a and B satisfy | a | = 2, | B | = 1, and a &; (a + b) = 3, then a, B =?
19. It is known that am is the middle line of BC in triangle ABC AM^2=1/2(AB^2+AC^2)-BM^2
20. Given the set M = {y | y = x & # 178; - 2x + 3}, n = {y | y = 2x & # 178; - 3x + 1}, then m ∪ n= Search process, online, etc