Question

The diagonal of a rectangle is of length a. It splits each corner forming two angles with a ratio of 1:2. The area of the rectangle is: Select one: a. 1/2 a^2 b. 1/4 a^2 c. 2a^2 d.sqrt 2/2a^2 e. sqrt 3/4a^2 f/ sqrt 3/4a^2

Answer 1

Answer:

Step-by-step explanation:

Given

Length of diagonal is a

Diagonal divides the angle in 1:2

such that $\theta +2\theta =90$ (because angle between two sides is 90)

$3\theta =90$

$\theta =30^{\circ}$

width of rectangle is $b=a\sin \theta =\frac{a}{2}$

Length of rectangle is $L=a\cos 30=\frac{\sqrt{3}}{2}a$

Area of rectangle $A=L\cdot b$

$A=\frac{\sqrt{3}}{2}a\times \frac{a}{2}$

$A=\frac{\sqrt{3}}{4}a^2$