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. V-belt
    remenice-a-remen1 Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
  2. The farmer
    field_2 The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
  3. Right triangles
    PT How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
  4. Ladder slope
    rebrik33 What is the slope of a ladder 6.2 m long and 5.12 m in height.
  5. Quatrefoil
    4listek Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
  6. Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  7. Circle - easy 2
    circle_3 The circle has a radius 6 cm. Calculate:
  8. Four circles
    circles_2 1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
  9. Two cyclists
    compass_1 Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?
  10. Garden
    zahon_4 Rectangular garden 31 meters 40 centimeters long and 20m30cm wide adjacent with the shorter side with another (fenced) garden and on one longest side is 1 meter wide gate. How many meters of fence is needed to buy? (Estimate, calculate, verify a test ca
  11. Cablecar
    petrin_draha Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb.
  12. Athlete
    sportovec How long length run athlete when the track is circular shape of radius 120 meters and an athlete runs five times in the circuit?
  13. Pulley
    kladka On wheels with a diameter of 40 cm is fixed rope with the load. Calculate how far is load lifted when the wheel turns 7 times?
  14. Octagonal mat
    8gon_1 Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
  15. Mirror
    mirror How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
  16. Internal angles
    angle_3 One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two other is 15°. Identify the size of these angles.
  17. Rectangle
    diagonal_rectangle_2 The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
  18. Right triangle eq2
    rt_2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
  19. Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  20. Rectangle - sides 4
    mouse Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also more information on Wikipedia.