Planimetry - problems

  1. 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.
  2. Square
    square_1 Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  3. Slope of track
    sklon_1 Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long.
  4. Tangents
    tangents To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre.
  5. Expansion
    magnification If one side of the rectangle is larger 3-times and second 4-times, what percentage increases the area of rectangle?
  6. Rectangle - sides ratio
    rectangle_2 Calculate area of rectangle whose sides are in ratio 1:7 and perimeter is 735.
  7. Medians
    medias_triangle Calculate the sides of a right triangle if the length of the medians to the legs are ta = 23 cm and tb=14 cm.
  8. R Trapezium
    Trapezium_example Rectangular trapezium has bases 17 and 7 and area 80 cm2. What is its perimeter?
  9. Rhombus
    rhombus_1 Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
  10. Hypotenuse and height
    euklides In a right triangle is length of the hypotenuse c = 45 cm and height hc = 19 cm. Determine the length of both trangle legs.
  11. Coins
    eur_coins Arnold had saved up a number of 1-euro coins. He stored coins in a single layer in a square. Left 4 coins. When he make square, which has one more row, missing 35 coins. How many euros he have?
  12. Trapezoid
    rectangular_trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
  13. Built-up area
    situacia_stavba John build up area 4.3 x 8 = 34.4 m2 with building with a wall thickness 50 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 8%?
  14. 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.
  15. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle.
  16. Euklid4
    euclid_2 Legs of a right triangle have dimensions 61 m and 39 m. Calculate the length of the hypotenuse and the height of this right triangle.
  17. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=100 cm.
  18. Garden plot
    plot Calculate how many meters of fence need to fence the square garden with length and width of 5 meters.
  19. Descent of road
    znacka_klesanie Road sign informs the gradient is 10.5%. Calculate the angle which average decreases.
  20. Distance
    distance Calculate distance between two points Z[7; -9] and U[-10; -8].

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