R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm2.

What is its perimeter?

Correct result:

p =  38.993 cm

Solution:

a=12 cm c=5 cm S=84 cm2  S=a+c2h  h=2 S/(a+c)=2 84/(12+5)168179.8824 cm b=h=9.8824168179.8824 cm  d=(ac)2+b2=(125)2+9.8824212.1104 cm  p=a+b+c+d=12+9.8824+5+12.1104=38.993 cma=12 \ \text{cm} \ \\ c=5 \ \text{cm} \ \\ S=84 \ \text{cm}^2 \ \\ \ \\ S=\dfrac{ a+c }{ 2 } h \ \\ \ \\ h=2 \cdot \ S / (a+c)=2 \cdot \ 84 / (12+5) \doteq \dfrac{ 168 }{ 17 } \doteq 9.8824 \ \text{cm} \ \\ b=h=9.8824 \doteq \dfrac{ 168 }{ 17 } \doteq 9.8824 \ \text{cm} \ \\ \ \\ d=\sqrt{ (a-c)^2+b^2 }=\sqrt{ (12-5)^2+9.8824^2 } \doteq 12.1104 \ \text{cm} \ \\ \ \\ p=a+b+c+d=12+9.8824+5+12.1104=38.993 \ \text{cm}



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