R Trapezium

Rectangular trapezium has bases 21 and 10 and area 92 cm². What is its perimeter?

Correct answer:

p =  49.4347 cm

Step-by-step explanation:

$$\begin{gathered} a=21\text{ cm } \\ c=10\text{ cm } \\ S=92{\text{cm}}^2 \\ S={\displaystyle \frac{a+c}{2}}h \\ h=2\cdot S\mathrm{/}(a+c)=2\cdot 92\mathrm{/}(21+10)={\displaystyle \frac{184}{31}}\doteq 5.9355\text{ cm } \\ b=h=5.9355={\displaystyle \frac{184}{31}}\doteq 5.9355\text{ cm } \\ d=\sqrt{(a-c{)}^2+b^2}=\sqrt{(21-10{)}^2+5.9355^2}\doteq 12.4992\text{ cm } \\ p=a+b+c+d=21+5.9355+10+12.4992=49.4347\text{ cm} \end{gathered}$$

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