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Find the area of the trapezoid in the figure below ground your final answer to the nearest 10th

Find The Area Of The Trapezoid In The Figure Below Ground Your Final Answer To The Nearest 10th class=

Sagot :

First, find the length of side CD.

[tex]\begin{gathered} CD=2CE+13.5 \\ \\ \text{By Pythagorean theorem} \\ CA^2=CE^2+AE^2 \\ CE^2=CA^2-AE^2 \\ CE^2=(30.5)^2-(26)^2 \\ CE^2=930.25-676 \\ CE^2=254.25 \\ CE=\sqrt[]{254.25} \end{gathered}[/tex][tex]\begin{gathered} CD=2CE+13.5 \\ CD=2(\sqrt[]{254.25})+13.5 \\ CD=31.89+13.5 \\ CD=45.39 \end{gathered}[/tex]

Now that we have length CD, recall that the area of the trapezoid is

[tex]\begin{gathered} A=\frac{a+b}{2}h \\ \text{where} \\ a\text{ is the top base} \\ b\text{ is the bottom base} \\ h\text{ is the height} \end{gathered}[/tex][tex]\begin{gathered} \text{Given} \\ h=AE=26 \\ a=CD=45.39 \\ b=AB=13.5 \\ \\ \text{Substitute these values to the formula and we have} \\ A=\frac{a+b}{2}h \\ A=\frac{45.39+13.5}{2}(26) \\ A=\frac{58.89}{2}(26) \\ A=(29.445)(26) \\ A=765.57 \end{gathered}[/tex]

Rounding the area to the nearest tenth, the area of the given trapezoid is equal to 765.6 square units.

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