One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.

Correct answer:

A =  1633.8636 m²

Step-by-step explanation:

$$\begin{gathered} a=24\text{ m } \\ b=36\text{ m } \\ c=80\text{ m } \\ d=80\text{ m } \\ x=c-a=80-24=56\text{ m } \\ s={\displaystyle \frac{x+b+d}{2}}={\displaystyle \frac{56+36+80}{2}}=86\text{ m } \\ {S}_1=\sqrt{s\cdot (s-x)\cdot (s-b)\cdot (s-d)}=\sqrt{86\cdot (86-56)\cdot (86-36)\cdot (86-80)}=60\sqrt{215}{\text{m}}^2\doteq 879.7727{\text{m}}^2 \\ {S}_1=xh\mathrm{/}2 \\ h=2\cdot S_1\mathrm{/}x=2\cdot 879.7727\mathrm{/}56\doteq 31.4205\text{ m } \\ A={\displaystyle \frac{a+c}{2}}\cdot h={\displaystyle \frac{24+80}{2}}\cdot 31.4205=1633.8636{\text{m}}^2 \end{gathered}$$

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Math student

m<abc = 60 degrees
m<def = 30 degrees

Are these angles complementary

4 months ago  Like

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