Calculate 20643

Calculate the area and perimeter of the building plot in the shape of an isosceles trapezoid with a base of 120 m, 95 m, and a height of 50 m.

Correct answer:

S =  5375 m²
o =  318.0776 m

Step-by-step explanation:

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

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

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