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. Flooring a room
    tiles_10 Find the cost of flooring a room 6.5 m by 5 m with square tiles of sides 25 cm at the rate of rupees 9.40 per tile.
  2. An equilateral
    goat__wolf_and_cabbage_1 An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?
  3. A photograph
    photo A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
  4. The perimeter 2
    quadrilateral_1 The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m?
  5. Two boats
    ship_1 Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
  6. Rectangular plot
    rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.
  7. A kite
    kite2 ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
  8. Area of a rectangle
    rectangle Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
  9. The tractor
    tractor The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m?
  10. Squares
    squares2 From a square of 12 dm perimeter is cut smaller square, whose side is the third side of the square. What is the area of the rest?
  11. Distance between 2 points
    axes2 Find the distance between the points (7, -9), (-1, -9)
  12. The Eiffel Tower
    Eiffel-Tower-Paris The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
  13. RPM
    motor_rpm An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
  14. The ladder
    rebrik The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
  15. The cable car
    lanovka The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?
  16. Company logo
    circle_square_insribed The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
  17. Tree trunk
    circle_and_square What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
  18. Isosceles triangle 9
    iso_triangle Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
  19. The second
    triangle The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
  20. Set of coordinates
    axes2 Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation?

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