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.

  1. Angles and sides of the triangle
    trig Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
  2. Plumber
    klempir Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
  3. Median
    medians.JPG In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
  4. Goat
    koza Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
  5. Triangle
    Triangle_trig Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
  6. Right angled triangle
    fun-triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
  7. RT and ratio
    triangles A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
  8. Around the flowerbed
    roses Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ro
  9. Isosceles trapezoid
    licho_1 Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
  10. Interesting property
    rectangles Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
  11. Circles
    pyt_theorem In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
  12. Square room
    kachlicky_1 What is the size of the smallest square room, which can pave with tiles with dimensions 55 cm and 45 cm? How many such tiles is needed?
  13. The sum graphically
    fun_1 Draw a graphically sum of the all sides of 4-gon ABCD.
  14. Rhombus
    pqrs PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.
  15. Trapezoid - diagonal
    licho Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
  16. ISO triangle
    rr Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
  17. Logs
    tramy The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
  18. Parallelogram ABCD
    paralleogram_1 The area of parallelogram ABCD is 440 cm2. Points M and N are the midpoints of the sides AB and BC. What is the area of a quadrilateral MBND?
  19. Parcel
    land_parcel Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage?
  20. Obtuse angle
    10979326_654459541349455_1236723697_n The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)

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