Q1-Each side of a rhombus has length equal to 1 and one of its angles is 45 degree. What is the area of the rh

Q1-Each side of a rhombus has length equal to 1 and one of its angles is 45 degree. What is the area of the rhombus?
(A)1
(B)1/square root 2
(C)1/2
(D)square root 2
(E) none

pls give full explanation

Your answer is 1/sqrt2.

If opposite angles are 45 deg each then other two angles are 135 deg

Draw the two diagonals then four triangles are formed which are equal in area
the three angles of this triangle are 22.5 , 67.5 and 90 deg

sin 22.5 and sin 67.5 form the base and height
area of that small triangle = (sin22.5 * sin67.5 )/2

Total area of rhombus = 4 * (sin22.5 * sin67.5 )/2
= 2*sin22.5*cos22.5
= sin45 = 1/sqrt2

Same 2u..

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Another angle is 135
then you have four triangles with hypotenuse=1
one angle=22.5 and the other 135/2=67.5
then sin 22.5=0.3827
cos 22.5=0.9238
area=4/2 sin22.5x1 x cos22.5x1=0.707
God bless you.

Answer D
Sorry the work I showed got deleted mainly figured it out by finding lengths of diagonals using sine formula a/sin(A)=b/sin(B)=c/sin(C) then multiply diagonals divide by 2 on.