Two 3 * 4 rectangles overlap. Find the area of the overlapping region (which is shaded).
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Pic added by Melody:
+118716 Two 3 * 4 rectangles overlap. Find the area of the overlapping region (which is shaded green).
tanα=34=0.75α=atan0.75≈36.8702α≈73.740sin73.74=3yy≈3sin73.74≈3.125GreenArea=2∗0.5∗y∗y∗sin(180−2α)GreenArea=y∗y∗sin(2α)GreenArea=y∗y∗3yGreenArea=y∗3GreenArea=3∗3.125GreenArea≈9.375u2
LaTex:
tan\alpha=\frac{3}{4}=0.75\\
\alpha=atan0.75\approx 36.87^0\\
2\alpha\approx 73.74^0\\
sin73.74=\frac{3}{y}\\
y\approx \frac{3}{sin73.74}\approx3.125\\
Green Area=2*0.5*y*y*sin(180-2\alpha)\\
Green Area=y*y*sin(2\alpha)\\
Green Area=y*y*\frac{3}{y}\\
Green Area=y*3\\
Green Area = 3*3.125\\
Green Area \approx 9.375u^2\\
+118716 You want it exact, you could have done it for yourself.
But here it is.
tanα=34=0.75α=atan0.75sin(2α)=3yy=3sin(2α)GreenArea=2∗0.5∗y∗y∗sin(180−2α)GreenArea=y∗y∗sin(2α)GreenArea=y∗y∗3yGreenArea=3yGreenArea=9sin(2α)GreenArea=92sinαcosαGreenArea=92∗35∗45GreenArea=9∗2524GreenArea=9.375
