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: 2168

  • The base 2
    cone The base diameter of a right cone is 16cm and it's slant height is 12cm. A. ) Find the perpendicular height of the cone to 1 decimal place. B. ) Find the volume of the cone, convert to 3 significant figure. Take pie =3.14
  • The ABCD
    trapezium The ABCD trapezoid has a base length of a = 120mm, c = 86mm and an area of S = 2575 mm2. Calculate the height of the trapezoid.
  • Calculate
    rr_triangle3 Calculate the height of an isosceles triangle with base 37.8 mm long and an arm 23.1 mm long.
  • The land
    land The land, which has dimensions of 220 m and 308 m, the owner wants to divide into equally large square plots with the largest possible area. How long will one side of the plot be?
  • Cuboid edges
    cuboid_3colors The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m2.
  • The pool
    bazen The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the bottom is 3 m greater than the other. What are the dimensions of the pool bottom?
  • Square gardens
    zahrada The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square.
  • Trapezoid 25
    rr_lichobeznik Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s.
  • Tractor wheels
    tractor The front wheel of the tractor has a circumference of 18 dm and the rear 60 dm. We will make a red mark on the lowest point of both wheels. The tractor then starts. At what distance from the start will both marks appear identically at the bottom again?
  • Gardens
    garden The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
  • Perpendicular projection
    lines Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.
  • The staircase
    schody The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
  • Ladder
    rebrik How long is a ladder that touches on a wall 4 meters high, and its lower part is 3 meters away from the wall?
  • Railway embankment
    rr_lichobeznik The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
  • The pyramid
    pyramid The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid.
  • Isosceles trapezoid
    rr_lichobeznik Find the area of an isosceles trapezoid with bases of 8cm and 72mm. The height of the trapezoid is equal to three-quarters of the longer base.
  • A cliff
    cliff A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the​ cliff, how high is the​ cliff?
  • Ten persons
    TUCWGKGHCVGBPEMEP75TVAR5LA Ten persons, each person makes a hand to each person. How many hands were given?
  • Rectangular garden
    zahrada Rectangular garden has a length of 48.7 m, a width of 6.3 meters shorter than the length. How much mesh should be bought for its fencing if the gate is 2.9 m long and the gate 1.1 m? What is the area of the garden?
  • Isosceles triangle
    rr_triangle3 Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.

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...



See also more information on Wikipedia.