Land - isosceles trapezoid

Calculate the building plot's content and perimeter in the form of an isosceles trapezoid with bases 120m, 95m, and height 50m.

Correct answer:

S =  5375 m²
o =  318.0776 m

Step-by-step explanation:

$$\begin{gathered} a=120\text{ m } \\ c=95\text{ m } \\ h=50\text{ m } \\ S=(a+c)\mathrm{/}2\cdot h=(120+95)\mathrm{/}2\cdot 50=5375{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} x=(a-c)\mathrm{/}2=(120-95)\mathrm{/}2={\displaystyle \frac{25}{2}}=12.5\text{ m } \\ b=\sqrt{h^2+x^2}=\sqrt{50^2+12.5^2}\doteq 51.5388\text{ m } \\ o=a+c+2\cdot b=120+95+2\cdot 51.5388=318.0776\text{ m} \end{gathered}$$

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