Answer:
Step-by-step explanation:
Given
Length of diagonal is a
Diagonal divides the angle in 1:2
such that [tex]\theta +2\theta =90[/tex] (because angle between two sides is 90)
[tex]3\theta =90[/tex]
[tex]\theta =30^{\circ}[/tex]
width of rectangle is [tex]b=a\sin \theta =\frac{a}{2}[/tex]
Length of rectangle is [tex]L=a\cos 30=\frac{\sqrt{3}}{2}a[/tex]
Area of rectangle [tex]A=L\cdot b[/tex]
[tex]A=\frac{\sqrt{3}}{2}a\times \frac{a}{2}[/tex]
[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]
