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. The sides 2
    trapezium_7 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
  2. Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  3. Lighthouse
    majak Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea.
  4. Find the 9
    obtuse_triangle_1 Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
  5. Trapezium diagonals
    stredova sumernost It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
  6. Isosceles triangle 8
    7-6-7-triangle If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
  7. Cable car
    lano_3 Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
  8. Area of rectangle
    rectangle_24 How many times will increase the area of the rectangle, if we increase twice the length and at the same time we decrease the width by the half?
  9. Horizontal distance
    road_2 The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
  10. Cincinnati
    Cincinnati A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth.
  11. A screen
    tv2_5 A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
  12. Right triangle
    rebrik_7 Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
  13. Velocipedes
    Velocipede In the 19th century, bicycles did not have a chain drive, and the pedals were connected directly to the wheel axis. This wheel diameter gradually increased until the so-called high bicycles (velocipedes) with a front wheel diameter of up to 1.5 meters, whi
  14. Triangle 42
    triangle2_4 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
  15. Hyperbola equation
    hyperbola_4 Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
  16. Rectangle
    rectangle_22 There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
  17. In the
    land_6 In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km2. What area is wooded?
  18. KLM triangle
    trojuholnik_8 Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
  19. Balloon and bridge
    hlbkovy_angle From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
  20. The size
    trapezium_6 The size of a Trapezium are 3/4×cm, ×cm 2(×+1)cm and 3(×+2)cm long respectively if it's perimeter is 60cm, calculate the length of each side.

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