Planimetrics - examples

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. One hectare
    land_1 How many square meters are one hectare?
  2. Rectangle - area, perimeter
    rectnagles_2 The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and witdh of this rectangle
  3. Special watch
    clocks2_20 Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?
  4. Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  5. Trevor
    tiles2_1 Trevor wishes to tile the floor of his bathroom. The bathroom is rectangular and is 4.2m long and 3.3m wide. The tiles are 30cm by 30cm. Calculate the cost to tile the floor if each tile costs 72 cents.
  6. Inscribed rectangle
    rectangle_inside_circle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
  7. Maria
    green-grapes Maria has decided to plant grapes in the garden behind her house. His neighbor Ben has grown grapes successfully for a long time and has given Maria advice on how to plant vines. Ben told her to plant them 3 meters apart in rows that are also 3 meters apar
  8. Decagon
    decanon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
  9. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  10. Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  11. Square to rectangle
    square_rot_2 What is the ratio of the area of a square of side x to the area of a rectangle of a rectangle of width 2 x and length 3
  12. Irrigation sprinkler
    postrekovac_1 The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can irrigate?
  13. SSA and geometry
    ssu_veta The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
  14. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  15. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  16. Find the 5
    distance-between-point-line Find the equation with center at (1,20) which touches the line 8x+5y-19=0
  17. A trapezoid
    trapezium_4 A trapezoid 75 ft wide on top 85 ft on the bottom, the height is 120 ft. What is its area in the square yds?
  18. Two people
    crossing Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar
  19. Garden
    garden_1 Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
  20. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.

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