IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.

Final Answer:

v =  27.7 cm
u=|AC|=|BD| =  43.1 cm

Step-by-step explanation:

$$\begin{gathered} a=37\text{cm} \\ c=29\text{cm} \\ r=28\text{cm} \\ x=(a-c)/2=(37-29)/2=4\text{cm} \\ v=\sqrt{r^2-x^2}=\sqrt{28^2-4^2}=16\sqrt{3}=27.7\text{cm} \end{gathered}$$

$u=\sqrt{v^2+(a-x{)}^2}=\sqrt{27.7128^2+(37-4{)}^2}=\sqrt{1857}=43.1\text{cm}$

Try another example