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. Diamond
    diamond_1 Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
  2. Triangle
    triangle_ABC_1 The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
  3. Hairs
    parochna Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it i
  4. Distance
    origin_math Wha is the distance between the origin and the point (18; 22)?
  5. Vector sum
    vectors The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
  6. Vectors
    vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
  7. Triangle
    triangle_inequality Determine if it is possible to construct a triangle with sides 28 31 34 by calculation.
  8. 6-gon
    hexagons Perimeter of regular hexagon is 113. Calculate its circumradius (radius of circumscribed circle).
  9. Leg
    tetris Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
  10. Diagonals
    diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
  11. Well
    well Rope with a bucket is fixed on the shaft with the wheel. The shaft has a diameter 50 cm. How many meters will drop bucket when the wheels turn 15 times?
  12. Inscribed rectangle
    circle_desc_rectangular The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
  13. Cosine
    theta Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
  14. ISO trapezium
    trapezium_2 Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
  15. CD disc
    CD_disc A compact disc has a diameter of 11.8 cm. What is the surface area of the disc in square centimeters?
  16. 30-60-90
    30-60-90 The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
  17. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  18. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  19. Diameter
    diameter_circle If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
  20. Combi-triangle
    komb_triangle On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?

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