The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.

Correct answer:

o =  22.2229 cm
S =  19.0681 cm2

Step-by-step explanation:

a=10 cm c=6 cm α=50  x=(ac)/2=(106)/2=2 cm  cosα=x:r  r=x/cos(α)=2/cos(50)=3.11145 cm  o=a+c+2 r=10+6+2 3.1114=22.2229 cm
tanα=h:x  h=x tan(α)=2 tan(50)=2.38351 cm  S=a+c2 h=10+62 2.3835=19.0681 cm2

We will be pleased if You send us any improvements to this math problem. Thank you!


Tips to related online calculators
See also our right triangle calculator.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

  • Ratio in trapezium
    lichobeznik_1 The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
  • Isosceles trapezoid
    rr_licho The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
  • Land - isosceles trapezoid
    lichobeznik-stredni_pricka_1 Calculate the building plot's content and perimeter in the form of an isosceles trapezoid with bases 120m, 95m, and height 50m.
  • ISO trapezoid v2
    lichobeznik bases of Isosceles trapezoid measured 20 cm and 4 cm and its perimeter is 55 cm. What is the are of a trapezoid?
  • Isosceles trapezoid
    rr_lichobeznik Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
  • Isosceles trapezoid
    lichobeznik Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
  • Isosceles
    rr_lichobeznik_1 Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
  • Right triangle
    rt_triangle It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
  • Rectangular trapezoid
    rt_licho The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
  • Isosceles triangle 10
    iso_23 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
  • Isosceles trapezoid
    lichobeznik_5 Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  • Diagonal
    trapezium_right_1 The rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has an area of 15 cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
  • Triangle SAS
    triangle_iron Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Trapezoid ABCD v2
    trapezium_table Trapezoid ABCD has a length of bases in ratio 3:10. The area of triangle ACD is 825 dm2. What is the area of trapezoid ABCD?
  • IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  • Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm
  • 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.