Find the value of x in the parallelogram calculator

Question

Parallelogram area = (height × AB) or (height × DC)

Lines AC and DB are called diagonals.
Diagonals bisect each other.
Diagonals are not equal.
Diagonals do not bisect the vertex angles.

Line 'h' is perpendicular to lines AB & DC and is called the height or altitude.

• BOTH pairs of opposite sides are equal.
AB = DC and AD = BC

• BOTH pairs of opposite angles are equal.
∠ A = ∠ C and ∠ B = ∠ D

• Adjacent angles are supplementary.
∠ A + ∠ D = ∠ D + ∠ C = ∠ C + ∠ B = ∠ B + ∠ A = 180°

• Each diagonal forms 2 congruent triangles.
Δ ADC = Δ ABC and Δ DAB = Δ DCB

The default setting is for 5 significant figures but you can change that by inputting another number in the box above.

Answers are displayed in scientific notation and for easier readability, numbers between .001 and 1,000 will be displayed in standard format (with the same number of significant figures.)
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This calculator computes the diagonals of a parallelogram and adjacent angles from side lengths and angles between sides.

It is done with the help of law of cosines

Check the picture. First, we use the law of cosines to find out d1, then we find the second angle of a parallelogram, which is , then we again use the law of cosines to find out d2. The remaining angles are found from the same law of cosines. After that, we find diagonal intersection angles using the fact that the sum of triangle angles is 180.

The polygon diagonals of a parallelogram

Calculation precision

Digits after the decimal point: 2

Second parallelogram angle

Area of a parallelogram given sides and angle

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[1] 2020/03/23 18:52 Under 20 years old / High-school/ University/ Grad student / A little /

Purpose of useGeometry Quiz.Comment/RequestCould you have put how you got the solution?

[2] 2019/07/14 14:58 40 years old level / Self-employed people / Useful /

Purpose of useCalculate area of parallelogram needed to build a fractile pattern for wooden art project.

[3] 2019/04/18 02:24 Under 20 years old / High-school/ University/ Grad student / A little /

Purpose of usePrecalc homeworkComment/RequestA step-by-step process showing users how to get from numbers to the answers.

[4] 2018/12/05 16:45 Under 20 years old / Others / A little /

Purpose of useworking out maths problem, gave me answer but no steps to get it

[5] 2018/11/22 03:22 Under 20 years old / Elementary school/ Junior high-school student / Very /

Purpose of useTo do my math homeworkComment/Requestit worked good

[6] 2018/04/12 04:28 Under 20 years old / High-school/ University/ Grad student / Very /

Purpose of useProgram

[7] 2018/01/18 12:09 Under 20 years old / High-school/ University/ Grad student / Not at All /

Purpose of useto slov my unknown questionsComment/RequestI cannot see the process it does it
You add a button below aleast for students who want to learn

[8] 2017/06/13 01:13 60 years old level or over / Self-employed people / Very /

Purpose of useFrom a site map that was a perfect parallelogram, verify square feet (and acreage). Comment/RequestTo the non math major units of measure and symbol syntax are always vexing. Would be great to have angle input in either decimal or degrees-minutes-seconds (not hard to convert but requires extra steps). Would also be good to have an Excel formula. In Excel, the Sin function requires input in Radians, so side1 * side2 * sin( pi() / 180 )

[9] 2017/03/26 10:00 Under 20 years old / High-school/ University/ Grad student / Useful /

Purpose of useMath revisionComment/Requesthow did you get the area with the given sides and angle? What was the method?from KeisanArea of a parallelogram = base * height = a*(b*sinθ)

[10] 2015/10/10 02:45 30 years old level / A teacher / A researcher / Very /

Purpose of useTo Know area of parallelogram given sides and angleComment/RequestIt is very easy and quick.

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