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Find the shaded area.

Note: The shaded area is a rectangle.

 

 Jun 19, 2020
 #1
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We have a 3-4-5 right triangle and a similar triangle with a hypotenuse of 3 units.

 

The longer leg of a smaller triangle:   3 / b = 5 / 4       b = (3 * 4) / 5  This is the width of the rectangle.

 

The length of the rectangle:        a = 5 - sqrt( 3² - b² )   smiley

 Jun 19, 2020
 #3
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A = ab    laugh

Guest Jun 19, 2020
 #2
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Find the shaded area.

 

 

  \(x:3=3:\sqrt{3^2+4^2}\\ x:3=3:5\\ 5x=9\\ x=\frac{9}{5}\)      \(the\ section\ at\ the\ bottom\ left\)

 

\(b:3=4:5\\ b=\frac{12}{5}\)                       \(width\)

\(a=5-x=5-\frac{9}{5}\\a=\frac{16}{5}\)          \(length\)

 

\(A=a\times b\\ A=\frac{16}{5}\cdot \frac{12}{5}\)

\(A=\frac{192}{25}=7.68\)

laugh  !

 Jun 19, 2020

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