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. 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.
  2. Trio 2
    decide Decide whether trio of numbers is the side of a right triangle: 26,24,10.
  3. 2d shape
    semicircles_rect Calculate the content of a shape in which an arbitrary point is not more than 3 cm from the segment AB. The length of the segment AB is 5 cm.
  4. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  5. Plot
    parcela_1 The plot on which Mr. Kalous is to build a house has the shape of a rectangle. On a 1: 500 scale, its dimensions are 7cm and 5.5cm. Find out the dimensions of the plot. Calculate the parcel size.
  6. Regular octagon
    220px-N_uholnik Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.
  7. Four ropes
    vysilac TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
  8. Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
  9. Diameters of circles
    circle5_1 How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
  10. Cableway
    cable-car Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
  11. Rounding
    map1 What width and length in centimeters may have rectangle land when round the dimensions to the meter , the width is 5 m and length 7 meters?
  12. Diagonals of diamond
    kosostvorec_4 Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
  13. Isosceles trapezoid
    rr_lichobeznik Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
  14. Parallelogram
    rovnobeznik_2 In the parallelogram we know one internal angle 67°33`. Calculate the other internal angles.
  15. Is right triangle
    triangle_1111_4 Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
  16. Ruler
    pravitko_1 How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
  17. Right triangle ABC
    right_triangle_2 Calculate the perimeter and area of a right triangle ABC, if you know the length of legs 4 cm 5.5 cm and 6.8 cm is hypotenuse.
  18. Land - isosceles trapezoid
    lichobeznik-stredni_pricka_1 Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
  19. Tree
    stromcek_1 Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
  20. Tree shadow 3
    tree3_1 A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ?

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