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. Rectangles
    rectangles2_3 How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm?
  2. Rectangle - area, perimeter
    rectnagles_2 The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
  3. Waste
    doska_kruh How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
  4. Inscribed rectangle
    rectangle_inside_circle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
  5. Square into three rectangles
    stvorcove-cisla_1 Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
  6. Three segments
    vysek_1 The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
  7. Right triangle
    rebrik_7 Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
  8. Depth angle
    cliff From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
  9. One hectare
    land_1 How many square meters are one hectare?
  10. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  11. Circle simple
    circles_3 Circumference of a circle is 6.28. What is the area of the circle?
  12. Perimeter of square
    stvorec_1 The square has a circumference 17cm. What is its area?
  13. Velocipedes
    Velocipede In the 19th century, bicycles did not have a chain drive, and the pedals were connected directly to the wheel axis. This wheel diameter gradually increased until the so-called high bicycles (velocipedes) with a front wheel diameter of up to 1.5 meters, whi
  14. Ladder
    rebrik33_4 Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
  15. Pavement
    chodnik2 Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
  16. An angle
    right_triangle_6 An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
  17. Special watch
    clocks2_20 Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?
  18. Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  19. Hexagon ABCDEF
    hexagon_2 In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
  20. Three sides
    triangle_vysky_2 Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .

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.