Trapezoid MO

The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other.

Calculate the perimeter and area of ​​the trapezoid.

Correct result:

p =  33.31
A =  69.25

Solution:

∣AC∣=12 ∣CD∣=8  sin⁡Θ=∣BC∣∣AC∣ cos⁡Θ=∣BC∣∣BD∣  cos⁡2Θ+∣CD∣∣AC∣cos⁡Θ−1=0 x2+∣CD∣∣AC∣x−1=0  x2+0.667x−1=0  a=1;b=0.667;c=−1 D=b2−4ac=0.6672−4⋅1⋅(−1)=4.4444444444 D>0  x1,2=−b±D2a=−0.67±4.442 x1,2=−0.33333333±1.05409255339 x1=0.720759220056 x2=−1.38742588672   Factored form of the equation:  (x−0.720759220056)(x+1.38742588672)=0   Θ=43∘52′58"  ∣BC∣=∣AC∣sin⁡Θ=8.31822608044 ∣AB∣=∣AC∣cos⁡Θ=8.64911064067 ∣AD∣=∣BC∣2+(∣AB∣−∣CD∣)2=8.34351423258  o=∣AB∣+∣BC∣+∣CD∣+∣AD∣=33.31
A=(∣AB∣+∣CD∣)⋅∣BC∣2=69.25

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