Planimetrics - 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. 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.
  2. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  3. 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?
  4. 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?
  5. 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.
  6. 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.
  7. 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?
  8. Complementary angles 2
    complementary_angles Two complementary angles are (x+4) and (2x - 7) find the value of x
  9. Equilateral triangle
    vpisany_stvorec A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
  10. Ruler and compass
    triangle_bac Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
  11. Coordinate axes
    tr_triangle_axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
  12. Trapezoid - intersection of diagonals
    intersect_trapezoid_diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
  13. Construct
    kosodlznik3 Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
  14. Sum of squares
    pytagorean The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
  15. Table
    stol_1 Find the circumference of the table, where the long side is 1.28 meters and the short side is 86 cm.
  16. Rectangle area
    rectangles_5 The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
  17. Inscribed circle
    vpisana2 Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
  18. ABCD square
    s1 In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
  19. Bamboo
    Bambus Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
  20. Two forces
    forces_1 The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.

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