Trapezoid MO

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.

Result

p =  33.31
A =  69.25

Solution:

AC=12 CD=8  sinΘ=BCAC cosΘ=BCBD  cos2Θ+CDACcosΘ1=0 x2+CDACx1=0  x2+0.667x1=0  a=1;b=0.667;c=1 D=b24ac=0.667241(1)=4.4444444444 D>0  x1,2=b±D2a=0.67±4.442 x1,2=0.33333333±1.0540925533895 x1=0.72075922005613 x2=1.3874258867228   Factored form of the equation:  (x0.72075922005613)(x+1.3874258867228)=0  Θ=435258"  BC=ACsinΘ=8.3182260804446 AB=ACcosΘ=8.6491106406735 AD=BC2+(ABCD)2=8.3435142325775  o=AB+BC+CD+AD=33.31|AC| = 12 \ \\ |CD| = 8 \ \\ \ \\ \sin \Theta = \dfrac{|BC|}{|AC|} \ \\ \cos \Theta = \dfrac{|BC|}{|BD|} \ \\ \ \\ \cos^2 \Theta + \dfrac{ |CD|}{|AC|}\cos \Theta - 1 =0 \ \\ x^2 + \dfrac{ |CD|}{|AC|}x - 1 =0 \ \\ \ \\ x^2 +0.667x -1 =0 \ \\ \ \\ a=1; b=0.667; c=-1 \ \\ D = b^2 - 4ac = 0.667^2 - 4\cdot 1 \cdot (-1) = 4.4444444444 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -0.67 \pm \sqrt{ 4.44 } }{ 2 } \ \\ x_{1,2} = -0.33333333 \pm 1.0540925533895 \ \\ x_{1} = 0.72075922005613 \ \\ x_{2} = -1.3874258867228 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -0.72075922005613) (x +1.3874258867228) = 0 \ \\ \ \\ \Theta = 43^\circ 52'58" \ \\ \ \\ |BC| = |AC| \sin \Theta = 8.3182260804446 \ \\ |AB| = |AC| \cos \Theta = 8.6491106406735 \ \\ |AD| = \sqrt{ |BC|^2 + (|AB|-|CD|)^2} = 8.3435142325775 \ \\ \ \\ o = |AB|+|BC|+|CD| + |AD| = 33.31
A=(AB+CD)BC2=69.25A = \dfrac{(|AB|+|CD|)\cdot |BC|}{2}= 69.25



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment:
#
Math student
How do you find the answer

avatar









Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. 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.
  2. The ditch
    prikop Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
  3. Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  4. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  5. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  6. Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  7. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
  8. The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  9. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  10. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  11. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  12. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  13. Unknown number 23
    cisla_4 Find 2/3 of unknown number, which is two thirds of the 99.
  14. Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160
  15. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  16. Trigonometry
    sinus Is true equality? ?
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?