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. AP RT triangle
    right_triangle_4 The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
  2. Two chords
    circle_chords There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
  3. Trapezium diagonals
    stredova sumernost It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
  4. Horizontal distance
    road_2 The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
  5. Irrigation sprinkler
    postrekovac_1 The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can irrigate?
  6. In the
    land_6 In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km2. What area is wooded?
  7. On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  8. Find the 3
    segment_2 Find the distance and mid-point between A(1,2) and B(5,5).
  9. Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  10. Square
    stvorec Square JKLM has sides of length 24 cm. Point S is the center of LM. Calculate the area of the quadrant JKSM in cm2.
  11. Sum of inner angles
    angle-sum-of-polygon Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
  12. Map scale
    mapa_14 The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
  13. Rectangular garden
    garden_21 The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
  14. Isosceles triangle 8
    7-6-7-triangle If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
  15. Circular arc
    obluk_1 Calculate the length of the circular arc if the diameter d = 20cm and the angle alpha = 142 °
  16. Diagonals of the rhombus
    kosostvorec_3 How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
  17. Triangles
    triangles_18 Hanka cut the 20 cm long straws into three pieces each piece had a length in cm. Then, with these three pieces, she tried to make a triangle. a) What circuit has each of the triangles? b) How long can the longest side measure? c) How many different trian
  18. Cable car
    lano_3 Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
  19. The big clock
    hodiny_4 The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00.
  20. Six-sided polygon
    hexagon-irregular In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.

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