Planimetrics - math 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: 2176

  • Coordinates of the intersection of the diagonals
    rectangle_inside_circle In the rectangular coordinate system, a rectangle ABCD is drawn. The vertices of the rectangle are determined by these coordinates A = (2.2) B = (8.2) C = (8.6) D = (2.6) Find the coordinates of the intersection of the diagonals of the ABCD rectangle
  • There
    triangle_rt_taznice There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a
  • The square
    ctverec_mo Calculate the area and perimeter of a square with side a = 15 dm S =, O =
  • Right triangle
    rt_ttt A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees.
  • Area and perimeter of rectangle
    rectnagles The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
  • Larger perimeter
    circle_and_square There are a square and a circle that passes through two adjacent vertices of the square (end points of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter?
  • Isosceles triangle
    rr_triangle3 In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
  • Find the
    12gon Find the content of a regular 12 sided polygon, if its side a = 12 cm.
  • Vertical rod
    shadow The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time.
  • The straight
    12perctent The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m?
  • Hectares
    mapa Determine the area of the rectangular land (in ha), which has dimensions of 3 cm and 4.5 cm on the plan with a scale of 1: 40,000.
  • Extending square garden
    garden_el Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m2 (square), it had the shape of a square again. How many meters has the length of each side of the garden been extended?
  • Gears
    bicycle_gears The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the bike's rear-wheel turn if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?
  • Natural fertilizer
    garden The rectangular garden measuring 120m and 60m was fertilized with 16kg of natural fertilizer. Natural fertilizer contains 45% organic matter. How much organic matter falls on 1 m2 of garden?
  • Poplar shadow
    shadow The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high?
  • Sphere in cone
    sphere_in_cone A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
  • Height
    triangle_rt1 The content of the triangle is 35 cm2. The length of the base is 10 cm. Determine the length of the height on the base.
  • How many
    steps2 How many 75 cm long steps will a football player take during training, when he runs on a 50m square track and goes around the course 3 times? We need writing, sketch, calculation. .. .
  • Dimensions of the trapezoid
    lichobeznik One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2
  • Chimney and tree
    shadow Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long.

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