2 years ago

How to do this problem?

Mathematics

1 answer:

solniwko [45]2 years ago

3 0

Count the units between the points

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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 rectan

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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 $A=L\cdot b$

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

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

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