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 answer:

o =  33.31
S =  69.25

Step-by-step explanation:

AC=12 CD=8  sin Φ = ACBC cos Φ = BDBC   cos2 Φ + AC CD cos Φ  1 =0  x2+CD/AC x1=0  x2+8/12 x1=0 x2+0.667x1=0  a=1;b=0.667;c=1 D=b24ac=0.667241(1)=4.4444444444 D>0  x1,2=2ab±D=20.67±4.44 x1,2=0.333333±1.054093 x1=0.72075922 x2=1.387425887  x=x1=0.72080.7208 Φ=arccosx=arccos0.72080.7659 rad Φ2=Φ  °=Φ π180   °=0.7659 π180   °=43.8828  °  BC=AC sin(Φ)=12 sin0.76598.3182 AB=AC cos(Φ)=12 cos0.76598.6491 AD=BC2+(ABCD)2=8.31822+(8.64918)28.3435  o=AB+BC+CD+AD=8.6491+8.3182+8+8.3435=33.31

Our quadratic equation calculator calculates it.

S=2(AB+CD) BC=2(8.6491+8) 8.3182=69.25

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