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:

$|AC| = 12 \ \\ |CD| = 8 \ \\ \ \\ \sin \Theta = \dfrac{|BC|}{|AC|} \ \\ \cos \Theta = \dfrac{|BC|}{|BD|} \ \\ \ \\ \cos^2 \Theta + \dfrac{ |CD|}{|AC|}\cos \Theta - 1 =0 \ \\ x^2 + \dfrac{ |CD|}{|AC|}x - 1 =0 \ \\ \ \\ x^2 +0.667x -1 =0 \ \\ \ \\ a=1; b=0.667; c=-1 \ \\ D = b^2 - 4ac = 0.667^2 - 4\cdot 1 \cdot (-1) = 4.4444444444 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -0.67 \pm \sqrt{ 4.44 } }{ 2 } \ \\ x_{1,2} = -0.33333333 \pm 1.05409255339 \ \\ x_{1} = 0.720759220056 \ \\ x_{2} = -1.38742588672 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -0.720759220056) (x +1.38742588672) = 0 \ \\ \ \\ \Theta = 43^\circ 52'58" \ \\ \ \\ |BC| = |AC| \sin \Theta = 8.31822608044 \ \\ |AB| = |AC| \cos \Theta = 8.64911064067 \ \\ |AD| = \sqrt{ |BC|^2 + (|AB|-|CD|)^2} = 8.34351423258 \ \\ \ \\ o = |AB|+|BC|+|CD| + |AD| = 33.31$
$A = \dfrac{(|AB|+|CD|)\cdot |BC|}{2}= 69.25$

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

Be the first to comment!

Following knowledge from mathematics are needed to solve this word math problem:

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. Garden
Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
2. Glasses
There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls?
3. Three glasses
Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the b
4. Pool
If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
5. Geography tests
On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
6. The escalator
I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I climb
7. Year 2020
The four-digit number divided by 2020 gives a result of 1, **. (Can not be in form 1,*0. ) Write all the options.
8. Sum of the digits
How many are two-digit natural numbers that have the sum of the digits 9?
9. 45th birthday
This year Mrs. Clever celebrated her 45th birthday. Her three children are now 7.11 and 15 years old. In how many years will Mrs. Clever's age be equal to the sum of her children's years?
10. Dividing money
Vilem, Cenek, and Edita divided the money they earned by spreading the leaflet. Vilem got 240 CZK more than Cenek and twice more than Edita. Edita got 400kc less than Vilem.
11. The tourist
The tourist traveled 78km in 3 hours. Part of the journey went on foot at 6km/h, the rest of the trip by bus at 30km/h. How long did he walk?
12. Brick weight
The brick weighs 2 kg and a half bricks. How much does one brick weigh?
13. Forestry workers
In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others, if they will work 10 hours a d
14. Three cats
If three cats eat three mice in three minutes, after which time 260 cats eat 260 mice?
15. Bonus
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
16. Troops
The route is long 147 km and the first-day first regiment went at an average speed of 12 km/h and journey back 21 km/h. The second day went second regiment the same route at an average speed of 22 km/h there and back. Which regiment will take route longe
17. Motion problem
From Levíc to Košíc go car at speed 81 km/h. From Košíc to Levíc go another car at speed 69 km/h. How many minutes before the meeting will be cars 27 km away?