# Planimetry - problems

1. Regular 5-gon
Calculate area of the regular pentagon with side 11 cm.
2. Gimli Glider
Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2080 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
3. Area of RT
Calculate the area of a right triangle which hypotenuse has length 20 and one hypotenuse segment has lenght 15.
4. Gear
Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?
5. Mast
Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
6. Right triangle
Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle.
7. Rectangle
In rectangle ABCD with sides |AB|=11, |AD|=12 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
8. Floor
The floor area of ​​the room is 29 m2 and has a width of 2 m. How many centimeters of circumference measured floor on the map at the scale 1:100?
9. Hexagon
There is regular hexagon ABCDEF. If area of the triangle ABC is 19, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
10. Diagonals of the rhombus
Calculate height of rhombus whose diagonals are 15 cm and 5 cm.
11. Circle
How big is area of circle if its circumference is 58.7 cm?
12. Chocolate
How many times should be broken chocolate consisting of 5 × 6 pieces to get the 30 parts?
13. Triangles
Equilateral triangle with side 25 cm has the same perimeter as an isosceles triangle with arm of 32 cm. Calculate the base x of an isosceles triangle.
14. Isosceles trapezium
Trapezoid NXTL (NX||TL) is isosceles. The size of the angle at vertex X is 60 degrees. Calculate the size of the angle at vertex T.
15. Euclid1
Right triangle has hypotenuse c = 15 cm. How large sections cuts height hc=7 cm on the hypotenuse c?
16. n-gon
Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
17. RT - hypotenuse and altitude
Right triangle TWS has hypotenuse s=202 km and altitude to s is 99 km. How long are hypotenuse segments?
18. Steeple
Steeple seen from the road at an angle of 57°. When we zoom out to 25 meters, it is seen at an angle of 21°. What is high?
19. Slope
What is the slope of a line with an inclination 1.06 rad?
20. Height
Is right that in any right triangle height is less or equal half of the hypotenuse?

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