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: 2136

  • The volleyball ball
    volejball The volleyball ball can have a circumference after inflation of at least 650 max 750 mm. What volume of air can this ball hold, if its circumference is the average of the minimum and maximum inflation of the ball.
  • Wallpaper
    net of cube 3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide?
  • Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
  • Rectangle 3-4-5
    diagonal_rectangle The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
  • Quadrilateral
    diamond In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
  • Area of iso-trap
    diagons-of-an-isosceles-trapezoid Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
  • Angles of a triangle
    triangles In triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
  • Right angle
    rt_triangle In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
  • Triangular prism
    hranol The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the prism's largest wall is 130 cm2, and the body height is 10 cm. Calculate the body volume.
  • Parallelogram
    rovnobeznik Calculate the area and perimeter of a parallelogram whose two sides are long a=24 cm b=22 cm and height ha = 6 cm long.
  • Tower
    pyramid2 Charles built a tower of cubes with an edge 2 cm long. In the lowest layer there were 6 cubes (in one row) in six rows, in each subsequent layer always 1 cube and one row less. What volume in cm3 did the whole tower have?
  • Two hemispheres
    hemisphere3 In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?
  • Construction of trapezoid
    lichobeznik Construct a trapezoid if b = 4cm, c = 7cm, d = 4,5cm, v = 3 cm (Procedure, discussion, sketch, analysis, construction)
  • Glass mosaic
    6gon How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.
  • Angles ratio
    3angle In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
  • Minute hand
    clocks What is the distance the minute hand of the clock travels in 12 minutes, if the diameter of the clock is 30 cm and the hand extends to a distance of 2 cm from the edge of the clock?
  • Pyramid
    jehlan_4b_obdelnik The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
  • The mast
    geodet The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
  • The garden
    zahrada The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €?
  • TV diagonal
    tv_diagonal Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?

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