Planimetry - examples

  1. Bicycle wheel
    cyklo2_2 After driving 157 m bicycle wheel rotates 100 times. What is the radius of the wheel in cm?
  2. Diagonals of a rhombus
    rhombus-diagonals_1 One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
  3. Right triangle eq2
    rt_2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
  4. Rhombus and diagonals
    kosostvorec_2 The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
  5. Is right?
    rtriangle Is triangle with sides 24, 51 and 45 right triangle?
  6. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  7. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  8. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
  9. It is rectangular?
    nice_3d Size of two of the angles in a triangle are: α=60°, β=20°. Is it a right triangle?
  10. Triangle
    eq_triangle Can be rectangular triangle equilateral?
  11. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
  12. Garden plot
    plot Calculate how many meters of fence need to fence the square garden with length and width of 5 meters.
  13. Height
    thales_law Is right that in any right triangle height is less or equal half of the hypotenuse?
  14. Triangle
    triangles Prove whether you can construct a triangle ABC, if a=5 cm, b=10 cm, c=2 cm.
  15. Trapezoid
    rectangular_trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
  16. Triangle P2
    1right_triangle Can triangle have two right angles?
  17. 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.
  18. Right Δ
    ruler Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  19. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  20. 3-bracket
    triangle2 May be the largest angle in the triangle less than 70°?

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