Isosceles trapezoid

In an isosceles trapezoid, the basic lengths are 15 cm and 9 cm. The diagonals are 13 cm long. Calculate the perimeter and area of the trapezoid.

Correct answer:

o =  35.6619 cm
S =  60 cm²

Step-by-step explanation:

$$\begin{gathered} a=15\text{cm} \\ c=9\text{cm} \\ u=13\text{cm} \\ x=\frac{a-c}{2}=\frac{15-9}{2}=3\text{cm} \\ {h}^2=u^2-(a-x{)}^2 \\ h=\sqrt{u^2-(a-x{)}^2}=\sqrt{13^2-(15-3{)}^2}=5\text{cm} \\ b=\sqrt{x^2+h^2}=\sqrt{3^2+5^2}=\sqrt{34}\text{cm}\doteq 5.831\text{cm} \\ d=b=5.831=\sqrt{34}\text{cm}\doteq 5.831\text{cm} \\ o=a+b+c+d=15+5.831+9+5.831=35.6619\text{cm} \end{gathered}$$

$S=\frac{a+c}{2}\cdot h=\frac{15+9}{2}\cdot 5=60{\text{cm}}^2$

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