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. Area of iso-trap
    diagons-of-an-isosceles-trapezoid Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
  2. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  3. A square
    rhombus3_3 A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
  4. Diagonals
    diagonals What x-gon has 54 diagonals?
  5. Rectangles
    rectangle_15 The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
  6. Find the 3
    segment_2 Find the distance and mid-point between A(1,2) and B(5,5).
  7. The length
    rectangle_14 The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
  8. Area of garden
    garden_20 If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
  9. Adding shapes
    rectangle_13 5 triangles + 1 square = how many sides in all
  10. Scale of plan
    zahrada_4 On the plan of the village in the scale of 1: 1000 a rectangular garden is drawn. Its dimensions on the plan are 25mm and 28mm. Determine the area of the garden in ares.
  11. A rectangle
    rectangle_12 A rectangle has an area of 36 cm2. What could the length and width of rectangle be?
  12. Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  13. Enlarged rectangle
    rectangle_10 The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
  14. Rhombus
    kosostvorec_1 The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
  15. Area of a triangle
    triangle1_2 What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3?
  16. Glass panel
    glass_4 A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
  17. Ratio of sides 2
    square_5 The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
  18. Garden
    garden_1 Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden?
  19. 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.
  20. Right Δ
    ruler Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.

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