Planimetrics - problems - page 35

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. Magic belt
    opasok The magic rectangular belt has the property that whenever its owner wants something, the length of the belt is reduced to 1/2 and the width to 1/3. After three such wishes, the belt had a content area 4 cm2. What was its original length if the original wid
  2. Playground
    plot_ihrisko.JPG Fencing square playground cost € 464; 1 meter cost € 19. What is the area of the playground?
  3. Angles in triangle
    angles_triangle.JPG Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees.
  4. The sum graphically
    fun_1 Draw a graphically sum of the all sides of 4-gon ABCD.
  5. Rectangle 3-4-5
    diagonal_rectangle_1 The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
  6. Triangle KLM
    klm_triangle In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
  7. Clock Tower
    clock_3 What angle is betwenn hands on Clock Tower when show 17 hours and 35 minutes?
  8. Interesting property
    rectangles Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
  9. Rectangle
    rectangles_3 The rectangle area is 182 dm2, its base is 14 dm. How long is the other side? Calculate its perimeter.
  10. Annulus
    medzikruzie Calculate the area of two circles annulus k1 (S, 3 cm) and k2 (S, 5 cm).
  11. Triangle
    heron1 Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
  12. The mast
    octagon A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
  13. Medians and sides
    taznice3 Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
  14. Triangle ABC v2
    triangles_4 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
  15. Math heart
    srdce_1 Stylized heart shape created from a square with side 5 cm and two semicircles over his sides. Calculate the content area and its circumference.
  16. Angle
    rightTriangle Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
  17. Isosceles trapezoid v3
    rovnobezky_uhly In an isosceles trapezoid ABCD is the size of the angle β = 81° Determine size of angles α, γ and δ.
  18. 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
  19. 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
  20. 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).

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