What's the area of a Rhombus with sides 5sqrt2, and a angle

Question

What's the area of a Rhombus with sides 5sqrt2, and a angle 45 degree?

july05 · Answer

2h^2=5^2*2 h=5 area=5*5sqrt2

mirhaque · Answer

That's the correct answer. Can you please explain?

AJB77 · Answer

I cannot see any easy way to do this without using trigonometry. Area of Rhombus = 2*Area of triangle. I used the formula:

Area of a triangle = b.c.sin(A)/2 where A is the angle included between sides b and c. Here b=c=5*sqrt(2) and A=45degrees => sin(A) = 1/sqrt(2)

christoph · Answer

the sides of a rhombus are equal. draw a line line from one bigger angle to the opposite base so that the line is perpendicular to the base. this smaller triangle is 1:1:sqrt2. height is 5 and the base is 5sqrt2. area of a rhombus is height * base = 5 * 5sqrt2 = 25sqrt2.

Arsene_Wenger · Answer

Agree Chris. A rhombus is like a ||gm with area = bs X ht. the base is given as 5 root 2, therefore, from 90-45-45, the opposite is 5, therefore area is 5 root 2 X 5 = 25 root 2.

gmat2me2 · Answer

Oops multipled by one more sqrt(2)

It is 25*sqrt(2)

What's the area of a Rhombus with sides 5sqrt2, and a angle

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