# Grade - examples - page 36

- Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S_{1}=190 dm^{2}and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Rhombus HP

Calculate area of the rhombus with height 24 dm and perimeter 12 dm. - Geometric mean

Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines. - Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm^{2}. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers. - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes? - Two runners

Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi - Tiles

From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles. - Supermarket cashiers

When at the supermarket are opened only 2 cash people waiting in the front approximately 12 minutes. How many will shorten the average waiting time in a front where supermarket open another three cashiers? - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 85 km, with regular train leave at 7:00 and arrive at 8:18, but train is late and has departure at 8:10 and arrive at 9:27. - Baker

The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough? - Icerink

Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water. - Aircraft

The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements. - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 12 cm and u_{2}= 10 cm. Prism height is twice base edge length. - ISO trapezium

Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees. - Fall

The body was thrown vertically upward at speed v_{0}= 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach? - Certificate

There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2? - Triangle TBC

TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB? - Truncated pyramid

How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm? - Lines

In how many points will intersect 14 different lines, where no two are parallel? - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3}. Calculate the volume, surface and diameter of the sphere.

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