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.

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