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A prism whose side edge is perpendicular to the bottom is called a straight prism. It is known that the bottom is a rhombic straight prism. Its volume diagonals are 9 and 15 respectively, and its height is 5
As shown in the figure, in abcd-a'b'c'd ', the two diagonals are a'c = 15cm, BD' = 9cm, and the side edges are AA '= DD' = 5cm. Both ∵ BDD 'and ∵ ACA' are right triangles. According to Pythagorean theorem, ac2 = 152-52 = 200, BD2 = 92-52 = 56, AC = 200 = 102, BD = 56 = 214 ∵
If the height of a regular hexagonal prism is 5cm and the longest diagonal is 13cm, its side area is______ ．
The height of the regular hexagonal prism is 5cm, the longest diagonal is 13cm, that is, the diagonal length of the bottom surface is 132 − 52 = 12cm, and the side length of the bottom surface is 6cm. Its side area is 6 × 5 × 6 = 180 (cm2), so the answer is 180cm2
In a regular quadrangular prism, the area of the bottom is 72 square cm, and the height is 5 cm
Don't just talk about drawing
√（2*72）=14cm
RELATED INFORMATIONS
- 1. The bottom surface of straight quadrangular prism ABCD --- a1b1c1d1 with height of 1 is a diamond with area of 2 The area sum of BDD 1B1 is 5, and the bottom edge length of the straight quadrangular prism is calculated
- 2. As shown in the figure, in the quadrilateral ABCD and the quadrilateral a1b1c1d1, if AB = A1B1, BC = b1c1, CD = c1d1, Da = d1a1, are the two quadrilateral congruent 1. XiaoCong's idea: connect diagonal AC and a1c1 respectively. If AC = a1c1, then The two quadrangles are congruent. According to Xiao Cong's idea, write the reasoning process 2. The teacher said that under the condition that the four sides of the quadrilateral are equal, Xiao Cong Add a condition - diagonal AC = a1c1, you can show congruence Please add another condition (except diagonal) to explain the congruence of the two quadrangles and write down your thinking process
- 3. In the cube abcd-a1b1c1d1 with edge length of 2, e is the midpoint of edge AB, and point P is in plane a1b1c1d1. If d1p ⊥ plane PCE, try to find the direction of line d1p My answer is 4 root 5 / 5 is correct?
- 4. It is known that the parallelepiped abcd-a'b'c'd ', e, F, G and H are the midpoint of edges a'd', d'c ', c'c and ab respectively. It is proved that e, F, G, h are coplanar
- 5. As shown in the figure, in the cube abcd-a1b1c1d1, if e and F are the midpoint of A1B1 and b1c1 respectively, then the angle between AD1 and EF is______ ．
- 6. In the cube abcd-a1b1c1d1, the cosine of the dihedral angle formed by plane a1bd and plane c1bd is () A. 12B. 13C. 32D. 33
- 7. In the cuboid abcd-a'b'c'd ', P and R are the moving points on BB' and CC ', respectively. When P and R satisfy what conditions, PR is parallel to the plane ab'd
- 8. As shown in the figure, in the cube abcd-a1b1c1d1, the tangent of the dihedral angle b-a1c1-b1 is___ ．
- 9. As shown in the figure, in the cuboid abcd-a1b1c1d1, ab = ad = 1, Aa1 = 2, and point P is the midpoint of dd1. Prove: (1) straight line BD1 ‖ plane PAC; (2) plane bdd1 ⊥ plane PAC; (3) straight line PB1 ⊥ plane PAC
- 10. As shown in the figure, the area of square ABCD is 16, △ Abe is an equilateral triangle, point E is in square ABCD, and there is a point P on diagonal BD, so that the sum of PC + PE is minimum, then the minimum value is () A. 4B. 23C. 26D. 2
- 11. A prism whose side edge is perpendicular to the bottom is called a straight prism. It is known that the bottom is a rhombic straight prism. Its volume diagonals are 9 and 15 respectively, and its height is 5
- 12. If the side length of diamond ABCD is 5cm and one diagonal is 6cm, the area of diamond ABCD is 5cm___ cm2．
- 13. In the cube abcd-a1b1c1d1 each vertex and each edge midpoint total 20 points, take any 2 points to form a straight line, take any one of these straight lines, the probability that it is perpendicular to the diagonal BD1 is () A. 21166B. 21190C. 18190D. 27166
- 14. As shown in the figure, the edge length of cube abcd-a1b1c1d1 is 4, M is the midpoint of BD1, n is on a1c1, and | A1N | = 3 | NC1 |, then the length of Mn is___ ．
- 15. The area of square ABCD is 200 square centimeters. Find the area of inscribed circle (π = 3.14)
- 16. As shown in the figure, P is a point on the diagonal BD of square ABCD
- 17. As shown in the figure, in the cube abcd-a1, B1, C1, D1 (1) Write the edges with point B as the endpoint respectively; (2) If an ant wants to climb from point a to vertex B, how can it get the shortest route? Why? (3) What if point a crawls along the surface to point C1?
- 18. In the cube abcd-a1b1c1d1, e, F and G are the midpoint of A1B1, b1c1 and B1B respectively
- 19. How can excel quickly classify ABCD in order of AA BB CC DD? Using Excel to sort~ For example: Data a: 123456 B：645679 C：456464 A：123455 B：668877 C：321457 . How to arrange for A: A: . B: B: . C: C: . This format. Please be more detailed
- 20. The parallelogram ABCD is known. The straight line FH intersects AB and CD. Through a, B, C and D, the perpendicular lines of FH are made. The perpendicular feet are e, h, G and F. verification: ae-df = cg-bh