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.

Number of problems found: 1947

  • Isosceles triangle
    isosceles-triangle-quilt Calculate the perimeter of isosceles triangle with arm length 73 cm and base length of 48 cm.
  • Three faces of a cuboid
    cuboid The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
  • Intersections
    intersect_circles How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
  • Průměr kužele
    cones Vypočtěte povrch a objem rotačního kužele jehož průměr je 60mm a délka strany 3.4 cm.
  • Circles
    SquareCircleSquare Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
  • Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  • Cut and cone
    kuzel Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
  • Circle chord
    circleChord What is the length x of the chord circle of diameter 115 m, if the distance from the center circle is 11 m?
  • Railways
    railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
  • Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  • Hypotenuse
    sqrt Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
  • Horizon
    lighthouse The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
  • Length 7
    square_numbers Length equals 7/6 inch in width equals 7/9 inches the area is?
  • Rhombus
    pqrs PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.
  • Sidewalk
    kruhovy-objazd The city park is a circular bed of flowers with a diameter of 8 meters, around it the whole length is 1 meter wide sidewalk . What is the sidewalk area?
  • Roof
    roof Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
  • Right angled triangle 3
    right_triangle_3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
  • Triangle midpoints
    sierpinski-geometry Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.

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



We will send a solution to your e-mail address. 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...
We encourage you to watch this tutorial video on this topic.



See also more information on Wikipedia.