Sine + area of shape - math problems

  1. 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.
  2. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  3. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  4. Pentagon
    5gon_3 Calculate the area of regular pentagon, which diagonal is u=17.
  5. Maximum area of rhombus
    rhombus Calculate the interior angles at which equilateral rhombus has a maximum area.
  6. Arc and segment
    odsek_kruh Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
  7. Angles
    rhombus_1 Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
  8. Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  9. Parallelogram
    paralleogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
  10. Goat and circles
    equation_nonlinear What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
  11. Jewel
    rhombus3 Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
  12. Rhomboid
    parallelogram Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
  13. Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  14. Black building
    talapka_cierna_stavba Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin
  15. Triangle KLB
    rovnostranny_trojuholnik It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
  16. ISO trapezium
    trapezium_2 Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
  17. Goat
    koza Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
  18. Triangle SAA
    triangle_blue The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
  19. SAS triangle
    triangles2 The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
  20. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.