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. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  2. Circular arc
    obluk_1 Calculate the length of the circular arc if the diameter d = 20cm and the angle alpha = 142 °
  3. Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  4. It is 2
    diamond_basetball It is 90 feet from home plate to first base on a baseball diamond. What is the area of the baseball diamond in square yards?
  5. The sides
    rectangle_9 The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
  6. A boy
    angles_6 A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
  7. Diamond diagonals
    kosostvorec Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
  8. Shadow of tree
    stromcek_3 Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
  9. Right angled triangle 3
    right_triangle_3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees
  10. Largest angle of the triangle
    obtuse_triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
  11. A bridge
    arc123 A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
  12. Equilateral triangle
    equilateral_triangle2_1 Calculate the area of an equilateral triangle with circumference 72cm.
  13. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  14. Rhombus 29
    rhombus3_2 One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
  15. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  16. Map scale
    mapa_14 The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
  17. Painters
    malovka2_3 Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
  18. Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
  19. A rectangular
    garden_19 A rectangular garden 40 m long and 30 m wide is to be fenced with fence posts at each corner. All the other posts will be 5 meters a part. How many posts will be needed to fence in the garden.
  20. Perimeter of a rectangle
    rectangle_4 If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?

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