# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

1. Boat A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
2. 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 S1=190 dm2 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.
3. Rhombus HP Calculate area of the rhombus with height 24 dm and perimeter 12 dm.
4. Rectangle The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
5. 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?
6. Tiles From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
7. 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.
8. 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.
9. 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?
10. Euclid3 Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.
11. Goat Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
12. Map - climb On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track?
13. Rectangle The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
14. Height Calculate height of the equilateral triangle if its perimeter is 8?
15. Isosceles trapezoid Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
16. Chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
17. Right trapezoid The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg.
18. Circle Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
19. Cable car 2 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
20. Railway Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?

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