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.
Instruction how to find the perimeter of a rectangular trapezium
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.
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.
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.
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).
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.
Fold the resulting values: P = AB + BC + CD + AD = b + c + b / sin (alpha) + a = a + b * (1 + 1 / sin (alpha) + c.