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The diagram below shows rectangle PLUM.
Find the area of rectangle PLUM.
If entering as a decimal round your final answer to the nearest hundredth.

 

 Apr 13, 2020
 #1
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Using Pythagoras theorem,

\((PL)^2=(AL)^2+(AP)^2\)

\(PL=\sqrt{(AL)^2+(AP)^2}\)

\(PL=\sqrt{64+36}=10\) units

Notice PL is the length of the rectangle.

 

Now,

Notice angle MPA, it is 45 degrees. Why? (PA  is perpendicular on diagonal LM) it follows, that it bisects the angle.

Notice triangle PAM is a right-angled triangle (LM is a straight line, the straight-line angle is 180 degrees, LAP is 90 so PAM is also 90 to add up to 180)

Use trigonometry to find PM

But From angle PMA (Which is also 45 degrees) (Angles in a triangle add up to 180 degrees)

\(sin(45)\frac{6}{PM}\)

Thus \(PM=\frac{6}{sin(45)}\)\(=8.485 units\)

Area of rectangle is PM*PL  (Length*width)

\(10*8.485\)

=\(84.85\) units squared, "round your final answer to the nearest hundredth" (already rounded)

 Apr 13, 2020

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