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. Ellipse
    elipsa Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
  2. Garden
    garden_18 The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?
  3. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  4. A map
    mapa_1 A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions?
  5. Area of garden
    garden_20 If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
  6. Inscribed circle
    vpisana2 Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
  7. The sides 2
    trapezium_7 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
  8. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  9. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  10. Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
  11. Each with each
    tenis_3 Five pupils from 3A class played table tennis. How many matches did they play with each other?
  12. Ratio of sides 2
    square_5 The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
  13. Rectangles
    rectangle_15 The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
  14. Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  15. Shadow
    shadow_1 A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
  16. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  17. Triangle perimeter
    triangle_vysky_3 Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
  18. Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
  19. Diagonals of a rhombus 2
    rhombus3_4 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
  20. Construct
    kosodlznik3 Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also more information on Wikipedia.