# Examples for secondary school students - page 39

1. Rhombus
One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
2. Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
3. Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
4. Tubes
Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?
5. Tray
Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
6. Annual income
The annual incomes (in thousands of \$) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean.
7. The city
In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
8. Square ABCD
Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
9. Diamond diagonals
Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
10. Average height
In a class are 34 students. The average height of students is 165 cm. What will be the average height of students in the classroom when two pupils tall 176 cm and 170 cm moved from this school/class?
11. James
James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
12. Win in raffle
The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
13. Equation
How many real roots has equation ? ?
14. Two triangles SSA
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
15. Hockey game
In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game?
16. Cleaners
Milan would clean up the room for 2.5 hours, Eric would take 10 hours. How long they swept the room together?
17. Prism
The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
18. Null points
Calculate the roots of the equation: ?
19. Crates 2
In 6 crates is 45 kg of apples In  5 crates is equally In 1 in crate is 3 kg more How many kilograms in each crate?
20. Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°).

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