Question

On one side of a square, a rhombus of the same side 'a' is
constructed. If one angle of the rhombus is 60 degrees, then the
area of the square not belonging to the rhombus is​

Answer 1

Answer:

The rhombus is made of 4 equal right-angled triangles.

Let such triangle have a hypothenuse of 1, a base of l and a height of s , with the angle between the base and the hypothenuse being α . Note that l=cosα and s=sinα , are the long and short, respectively, half-diagonal of the rhombus. The area of the square with length 1 will be 1, the area of the rhombus is then supposed to have area 12 .

4⋅l⋅s2=2sinαcosα=sin(2α)=12

From this it follows that

α=12⋅arcsin12=π12=15∘

The ratio between l and s , which is the ratio between the long and short half-diagonal of the rhombus, is

ls=cosαsinα=cotα=cotπ12=3.73205

Answer 2

Answer:

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Explanation:

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