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

  • Draw triangle
    iso_51 Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm.
  • Trapezoid
    lichob_2_1 How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
  • Rectangles
    strihanie Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
  • Flakes
    kvietok_MO A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
  • An equilateral
    rs_triangle2 An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
  • Slant height
    cone_10 The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
  • Body diagonal
    cuboid Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
  • Jewel
    rhombus3 Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
  • Triangular prism
    prism_rt Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
  • Combi-triangle
    komb_triangle On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
  • Euclid theorems
    euklidova_veta_trojuhelnik_nakres Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
  • Diagonals of a rhombus 2
    rhombus3_4 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
  • Interior angles
    circle_inscribed_polygon In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
  • Chord AB
    chord_3 What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
  • Medians in triangle
    stredne_pricky Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm.
  • 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.
  • Angle of two lines
    ihlan There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
  • Square and circles
    squares_cut_circles The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
  • Garden
    garden_18 The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?
  • Quadrilateral pyramid
    jehlan_4b_obdelnik Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.

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