what the area of rhombus having all sides equal to 8cm each and one pair of angles equal to 60°?
Answer (1)
22nd Mar, 2020
Hello,
To calculate the area of Rhombus you first need to find the diagonal.
All the sides of Rhombus are equal and measure 8 cm.
We all know that if all the sides of Rhombus is equal then its diagonal is also equal.
If you draw the Rhombus on paper along with its diagonals you will see that there are two equilateral triangles because two sides are equal and angle between them is 60 degree.
Height of an equilateral triangle is 3/2 multiplied by side
So, the diagonals will be ( 3/2) x 8 = ( 0.866 x 8 ) = 6.928 cm
Now to Calculate the Area of Rhombus use the formula - 1/2 D.( 4s -D)
where s side of Rhombus = 8 cm and D = diagonal of Rhombus = 6.928 cm.
Therefore putting the values in formula, we get
= 1/2 x 6.928.( 4 x (8) - (6.928))
= 1/2 x 6.928.( 4 x 64 - 47.997)
= 1/2 x 6.928.( 256-47.997)
= 1/2 x 6.928.( 208.003)
= 1/2 x 6.928 x 14.422
= 99.917/2
= 49.958 cm sq..
So, The Area of Rhombus Having All Sides Equal to 8 cm and one pair of angles equal to 60 degree is 49.958 cm sq .
Approximately it can said that Area of given Rhombus is 49.96 cm sq..
Hope this was helpful.
To calculate the area of Rhombus you first need to find the diagonal.
All the sides of Rhombus are equal and measure 8 cm.
We all know that if all the sides of Rhombus is equal then its diagonal is also equal.
If you draw the Rhombus on paper along with its diagonals you will see that there are two equilateral triangles because two sides are equal and angle between them is 60 degree.
Height of an equilateral triangle is 3/2 multiplied by side
So, the diagonals will be ( 3/2) x 8 = ( 0.866 x 8 ) = 6.928 cm
Now to Calculate the Area of Rhombus use the formula - 1/2 D.( 4s -D)
where s side of Rhombus = 8 cm and D = diagonal of Rhombus = 6.928 cm.
Therefore putting the values in formula, we get
= 1/2 x 6.928.( 4 x (8) - (6.928))
= 1/2 x 6.928.( 4 x 64 - 47.997)
= 1/2 x 6.928.( 256-47.997)
= 1/2 x 6.928.( 208.003)
= 1/2 x 6.928 x 14.422
= 99.917/2
= 49.958 cm sq..
So, The Area of Rhombus Having All Sides Equal to 8 cm and one pair of angles equal to 60 degree is 49.958 cm sq .
Approximately it can said that Area of given Rhombus is 49.96 cm sq..
Hope this was helpful.
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