Instruction

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**The perimeter**of a rectangular

**trapezoid**equal to the sum of the lengths of the sides of the two bases and two sides. Task 1. Find the perimeter of a rectangular

**trapezoid**, if the lengths of all its sides. To do this, add up all four values: P (perimeter) = a + b + c + d.This is the easiest way to find the perimeter problems, other initial data, in the end, it boils down to it. Let's consider the options.

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Task 2.Find the perimeter of a rectangular

**trapezoid**, if you know the bottom base AD = a, not perpendicular to it side CD = d, and the angle at this side of the ADC is equal to alpha.Solution.Guide the height**of the trapezoid**from vertex C is on the larger base, get the CE segment, trapezoid split into two pieces - a rectangle ABCE and right triangle ECD. The hypotenuse of the triangle is known to us side**of the trapezoid**CD, one of the legs is equal to is perpendicular to the side**of the trapezoid**(rule rectangle two parallel sides equal to AB = CE), and another segment whose length is equal to the difference between the bases**of the trapezoid**ED = AD - BC.3

Find the sides of a triangle: according to the existing formula CE = CD*sin(ADC) and ED = CD*cos(ADC).Now calculate the upper base - BC = AD - ED = a - CD*cos(ADC) = a - d*cos(alpha).Find out the length of the perpendicular sides AB = CE = d*sin(alpha).So you've got the lengths of all sides of a rectangular

**trapezoid**.4

Fold the values obtained, it will be a rectangular perimeter

**of a trapezoid**:P = AB + BC + CD + AD = d*sin(alpha) + (a - d*cos(alpha)) + d + a = 2*a + d*(sin(alpha) cos(alpha) + 1).5

Task 3.Find the perimeter of a rectangular

**trapezoid**, if the lengths of its bases AD = a, BC = c, the length of the perpendicular sides AB = b and the acute angle at the other side ADC = the alpha.Solution.Spend the perpendicular CE will receive a rectangle ABCE and a triangle CED.Now find the length of the hypotenuse of the triangle CD = AB/sin(ADC) = b/sin(alpha).So you've got the lengths of all sides.6

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