How To Find The Perimeter Of A Rectangular Trapezium | The Science

 

 

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How to find the perimeter of a rectangular trapezium

Trapeze - quadrangle with two parallel bases and is non-parallel sides. Rectangular trapezoid has a right angle at one side.

How to find the perimeter of a rectangular trapezium

Instruction how to find the perimeter of a rectangular trapezium

Step 1:

The perimeter of the rectangular trapezoid is equal to the sum of the lengths of the sides of the two bases and two sides. Problem 1. Find the perimeter of a rectangular trapezoid, if you know the length of its sides. To do this, put all four values: P (perimeter) = a + b + c + d.Eto easiest option of finding the perimeter, the problem with the other initial data, in the end, come down to it. Consider the options.

Step 2:

Task 2.Locate perimeter of a rectangular trapezoid, if we know the lower base AD = a, it is not perpendicular to the side CD = d, and the angle at that side of the ADC is equal to the height of the trapezoid Alfa.Reshenie.Provedite from vertex C to the larger base, we obtain CE segment , trapezoid divided into two shapes - rectangle ABCE and angled triangle ECD. The hypotenuse of the triangle - is known to us side trapezoid CD, one of the legs is perpendicular to the side of the trapezoid (the rule rectangle two parallel sides equal - AB = CE), and the other - a segment whose length is equal to the difference of the trapezium bases ED = AD - BC.

Step 3:

Locate the legs of the triangle: There is a formula for CE = CD * sin (ADC) and ED = CD * cos (ADC) .Now calculate upper base - BC = AD - ED = a - CD * cos (ADC) = a - d * cos (Alpha) .Uznayte length perpendicular to the side - AB = CE = d * sin (alpha) .Itak you got the lengths of all sides of the rectangular trapezoid.

Step 4:

Add up the values ​​obtained, it will be the perimeter of a rectangular trapezoid: P = AB + BC + CD + AD = d * sin (alpha) + (a - d * cos (alpha)) + d + a = 2 * a + d * ( sin (alpha) - cos (alpha) + 1).

Step 5:

Task 3.Find perimeter of a rectangular trapezoid, if you know the length of its base AD = a, BC = c, perpendicular to the length of the side AB = b, and an acute angle at the other side of the ADC = Alfa.Reshenie.Provedite CE perpendicular get ABCE rectangle and triangle CED.Teper get the length of the hypotenuse of the triangle CD = AB / sin (ADC) = b / sin (alpha) .Itak you got the lengths of all sides.

Step 6:

Fold the resulting values: P = AB + BC + CD + AD = b + c + b / sin (alpha) + a = a + b * (1 + 1 / sin (alpha) + c.