RR trapezoid

Given an isosceles trapezoid ABCD with bases |AB| = 36 m and |CD| = 200 dm, and leg |BC| = 10 m. Calculate the area and perimeter of the trapezoid and the length of diagonal AC.

Final Answer:

S =  168 m²
o =  76 m
u =  28.6356 m

Step-by-step explanation:

$$\begin{gathered} a=36\text{m} \\ c=200\text{dm}\to \text{m}=200:10\text{m}=20\text{m} \\ b=10\text{m} \\ x=\frac{a-c}{2}=\frac{36-20}{2}=8\text{m} \\ {x}^2+h^2=b^2 \\ h=\sqrt{b^2-x^2}=\sqrt{10^2-8^2}=6\text{m} \\ S=\frac{a+c}{2}\cdot h=\frac{36+20}{2}\cdot 6=168{\text{m}}^2 \end{gathered}$$

$o=a+2\cdot b+c=36+2\cdot 10+20=76\text{m}$

$u=\sqrt{(a-x{)}^2+h^2}=\sqrt{(36-8{)}^2+6^2}=2\sqrt{205}=28.6356\text{m}$

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