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The edge length of cube abcd-a1b1c1d1 is a, and the area of triangle ab1d1 is calculated The edge length of cube abcd-a1b1c1d1 is a, (1) the area of triangle ab1d1, (2) the area of triangular pyramid a1-abd, (3) the sine value of the angle between straight line AC1 and plane ABCD
1. Ab1 = AD1 = b1d1 = root 2 × a, area is a ^ 2 / 2 × root 3
2. The volume of a1-abd is a ^ 2 / 2 × a × 1 / 3 = a ^ 3 / 6
3. CC1 ⊥ ABCD, AC1 length is a × root 3, so the sine value is 1 / root 3
It is known that the edge length of the cube abcd-a1b1c1 is a, and its four non adjacent vertices a, B1, C and D1 form a tetrahedron. The volume of the tetrahedron is calculated
Important map, detailed explanation ~ ~ ~ ~ ask for help~~~~~
It is easy to get that the side length of the regular tetrahedron is √ 2a, but it is easy to get that the distance between the point B1 and the point D and the plane ad1c is equal. The cube diagonal b1d = √ (a ^ 2 + A ^ 2 + A ^ 2) = √ 3a, so the height of the regular tetrahedron = √ 3A / 2, and the area of the base of the regular tetrahedron = (1 / 2) · (√ 2a) · (√ 6A / 2) = (√ 3A ^ 2) / 2
RELATED INFORMATIONS
- 1. In the cube abcd-a1b1cid1, M is the midpoint of CC1, AC intersects BD at O, and it is proved that a1o is perpendicular to the plane MBD How to prove that a1o is perpendicular to BD, BM
- 2. In the cube abcd-a1b1c1d1, M is the midpoint of Aa1
- 3. In the cube abcd-a1b1c1d1, M is the midpoint of Aa1 ditto
- 4. As shown in the figure, in the cube ABCD – a1b1c1d1, verify that plane aca1c1 is perpendicular to plane a1bd
- 5. Make a plane intersection aa1d1d through the edge BB1 of square abcd-a1b1c1d1, and verify: EF / / BB1
- 6. In cube ABCD_ In a1b1c1d1, if the edge length is a, P is the midpoint of edge Aa1, and Q is any point on edge BB1, then the minimum value of PQ + QC is?
- 7. In the cube abcd-a1b1c1d1, e is the midpoint of d1d, f is the midpoint of AB, and EC is at an angle with FB1
- 8. As shown in the figure, the square prism abcd-a1b1c1d1 is known, the point E is the midpoint of edge d1d, A1A = radical 2a, ab = A. (1) verification: D1
- 9. As shown in the figure, in the four prism abcd-a1b1c1d1, d1d ⊥ bottom surface ABCD, bottom surface ABCD is square, and ab = 1, d1d = 2. (1) find the angle between the line D1b and the plane ABCD; (2) prove: AC ⊥ plane bb1d
- 10. In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, then In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, the area of quadrilateral a1b1c1d1 is ()
- 11. It is known that in the cube abcd-a1b1c1d1, the edge length is 1 and the area of triangle a1bc is calculated
- 12. For a cube with shuttle length of 2, in ABCD A1 B1 C1 D1, M is the middle point of edge Aa1, and the area of the cross section is 0 The answer is 9 / 2 I don't know. The answer in the book is 9 / 2
- 13. (1) In the cube abcd-a1b1c1d1, e and F are the moving points on edges BB1 and CC1 respectively, ab = 1. The volume of the tetrahedron with vertices a, C, B1 and D1 is calculated RT
- 14. In the cube abcd-a1b1c1d1, e and F are the midpoint of dd1 and DB, respectively
- 15. In the cube abcd-a1b1c1d1, e is the midpoint of CC1, AC ∩ BD = 0
- 16. In the cube abcd-a.b.c.d., e is the midpoint of AA. Proof: A.C flat plane BDE
- 17. It is known that in the cube abcd-a1b1c1d1, e and F are the midpoint of CC1 and Aa1 respectively
- 18. As shown in the figure, in the cube abcd-a1b1c1d1, M is the midpoint of CC1, AC intersects BD at point O, proving: a1o ⊥ plane MBD
- 19. The length of a right angle side of a right triangle a = 2 root sign 2, the length of hypotenuse C = 4 root sign 5
- 20. The relationship between the sides of 45 degree right triangle