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. Hřiště
    playground Map scale is 1: 5000. The playground is rectangular and on the map has dimensions 10 cm and 5 cm What is area of playground in square meters in reality?
  2. Climb
    aircraft_ascend For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand).
  3. Hexagon 5
    hexagon_1 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
  4. Playground
    plot_ihrisko.JPG Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground?
  5. Snowman 2
    snowman_1 On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles expres
  6. Cosine
    cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
  7. Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  8. Diagonals in the diamond
    kosoctverec_color The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
  9. Snowman
    snehuliak_1 In a circle with a diameter 50 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman.
  10. Saw
    bosh_saw Blade circular saw with a diameter 42 cm turns 825 times per minute. Expresses his cutting speed in meters per minute.
  11. Quadrilateral
    diamond_2 In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
  12. Euclidean distance
    euclidean Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
  13. Wheel
    wheel How many times turns the wheel of a passenger car in one second if car run at speed 100 km/h. Wheel diameter is d = 62 cm.
  14. Rotatable tower
    veza Rotatable tower situated in the city center has ground shape of a regular polygon. If the tower is rotated by 14.4° around its centerpiece it looks from the side same. Your task is to calculate at least how many vertices can have a ground plan view of the
  15. KLMN
    trapezium In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
  16. Park
    park_voda In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
  17. Rectangle - sides 3
    stvorec If in the rectangle ABCD we enlarge the side a by 5 cm and decrease the side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of the side a by 4 cm and and at the same time we increase the length of side b by 3 cm we inc
  18. RT 11
    right_triangle Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
  19. Ladder
    studna 8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
  20. Tiles
    dlazdice From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.

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