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.

Correct result:

p =  33.31
A =  69.25

Solution:

$|AC| = 12 \ \\ |CD| = 8 \ \\ \ \\ \sin \Theta = \dfrac{|BC|}{|AC|} \ \\ \cos \Theta = \dfrac{|BC|}{|BD|} \ \\ \ \\ \cos^2 \Theta + \dfrac{ |CD|}{|AC|}\cos \Theta - 1 =0 \ \\ x^2 + \dfrac{ |CD|}{|AC|}x - 1 =0 \ \\ \ \\ x^2 +0.667x -1 =0 \ \\ \ \\ a=1; b=0.667; c=-1 \ \\ D = b^2 - 4ac = 0.667^2 - 4\cdot 1 \cdot (-1) = 4.4444444444 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -0.67 \pm \sqrt{ 4.44 } }{ 2 } \ \\ x_{1,2} = -0.33333333 \pm 1.05409255339 \ \\ x_{1} = 0.720759220056 \ \\ x_{2} = -1.38742588672 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -0.720759220056) (x +1.38742588672) = 0 \ \\ \ \\ \ \\ \Theta = 43^\circ 52'58" \ \\ \ \\ |BC| = |AC| \sin \Theta = 8.31822608044 \ \\ |AB| = |AC| \cos \Theta = 8.64911064067 \ \\ |AD| = \sqrt{ |BC|^2 + (|AB|-|CD|)^2} = 8.34351423258 \ \\ \ \\ o = |AB|+|BC|+|CD| + |AD| = 33.31$

$A={\displaystyle \frac{(\mathrm{\mid }AB\mathrm{\mid }+\mathrm{\mid }CD\mathrm{\mid })\cdot \mathrm{\mid }BC\mathrm{\mid }}{2}}=69.25$

Try another example

Showing 1 comment:

Math student

How do you find the answer

10 months ago  Like

Next similar math problems:

• Discriminant
  Determine the discriminant of the equation: ?
• Solve 3
  Solve quadratic equation: (6n+1) (4n-1) = 3n²
• Roots
  Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Equation
  Equation ? has one root x₁ = 8. Determine the coefficient b and the second root x₂.
• Quadratic equation
  Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
• The product
  The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
• Roots count
  Substitute the numbers/0,1,2,3/into the equation as x: (x - 1) (x - 3) (x + 1) = 0 Which of them is its solution? Is there another number that solves this equation?
• Trigonometry
  Is true equality? ?
• Unknown number 23
  Find 2/3 of unknown number, which is two thirds of the 99.
• Variable
  Find variable P: PP plus P x P plus P = 160
• Find the 20
  Find the product and the sum of the roots of x² + 3x - 9 = 0
• Catheti
  The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
• One side
  One side is 36 long with a 15° incline. What is the height at the end of that side?
• Isosceles trapezoid
  Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
• Trapezoid IV
  In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
• The right triangle
  In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
• Right
  Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?