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. Rhombus
    rhombus2_3 The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
  2. Circle chord
    tetiva Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
  3. Similarity coefficient
    eqlateral_triangles The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
  4. Rhombus
    rhombus_4 Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm.
  5. Right angled
    right-triangle From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
  6. Isosceles trapezoid
    lichobeznik Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
  7. Areaf of ST
    triangle-inside-square It is given square DBLK with side |BL|=13. Calculate area of triangle DKU if vertex U lie on line LB.
  8. Garden
    plot_1 Rectangular garden has a length 99 m and width 84 m. Calculate how many m2 will decrease its area if land by ornamental fence with width 30 cm.
  9. Circle arc
    arc_cut Calculate the area of the circular arc in m2 where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.
  10. 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?
  11. Hexagon
    hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
  12. Isosceles III
    demos The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
  13. Leg and height
    right_triangles Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
  14. Without Euclid laws
    euclid_1 Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
  15. Angles in a triangle
    fun The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
  16. Geodesist
    XY Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
  17. XY triangle
    triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
  18. Isosceles triangle
    math_fun_1 What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m.
  19. Chocholate
    chocolate-xy-axis Table of chocolate is divided into squares on its surface. Lengthwise has 15 squares and widthwise 19 squares. We must chocolate broke into individual squares. How many times we have broke it to get only individual squares? It is not permitted to brea
  20. Goniometric form
    complex_fnc Determine goniometric form of a complex number ?.

Do you have an interesting mathematical word problem that you can't solve it? Submit 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...


See also more information on Wikipedia.