Consider 3

Consider the isosceles trapezoid PQRS. The bases are |PQ|=120 mm, |RS|=62 mm and the arm s=48 mm. Find the height of the trapezoid, diagonal length and the area of the trapezoid.

Correct answer:

h =  38.2492 mm
d =  98.7117 mm
A =  3480.6757 mm²

Step-by-step explanation:

$$\begin{gathered} a=120\text{mm} \\ c=62\text{mm} \\ b=48\text{mm} \\ d=b=48\text{mm} \\ x=(a-c)/2=(120-62)/2=29\text{mm} \\ {b}^2=h^2+x^2 \\ h=\sqrt{b^2-x^2}=\sqrt{48^2-29^2}=\sqrt{1463}=38.2492\text{mm} \end{gathered}$$

$$\begin{gathered} d^2=h^2+(a-x{)}^2 \\ d=\sqrt{h^2+(a-x{)}^2}=\sqrt{38.2492^2+(120-29{)}^2}=4\sqrt{609}=98.7117\text{mm} \end{gathered}$$

$A=\frac{a+c}{2}\cdot h=\frac{120+62}{2}\cdot 38.2492=91\sqrt{1463}=3480.6757{\text{mm}}^2$

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