A parallelogram with opposite equal acute and obtuse angles and four equal sides.
Diagonals
4 equal sides
Diagonals

h b
Same as Area of parallelogram
A = b .
h

Since the diagonals are perpendicular
Another way to find the area of a rhombus is:
Area = ½ (product of the diagonals) area = ½ (d
1
.
d
2
)
This is good when you only know the diagonals, but not the sides or height

The formula for the area of a rhombus can be justified using the area of a triangle. A specific case follows.
The diagonals divide a rhombus into 4 congruent right triangles. So, the area of the rhombus is 4 times the area of one of the right triangles.
Area of 1 triangle = 1/2bh = ½( 3 )( 4 ) = 6
Area of 4 triangles = 4(6) = 24
Notice that 1/2d equals 24
1 d
2 or ½(6)(8), also

Example 3 Find the Area of a Rhombus
Find the area of the rhombus.
a.
b.
SOLUTION a.
1
A = d
2 1 d
2
=
1
2
(14)(10)
= 70
The area of the rhombus is 70 square inches.
SOLUTION b.
A =
1
2 d
1 d
2
=
1
2
(6 + 6)(9 + 9)
=
1
2
(12)(18)
= 108
The area of the rhombus is 108 square inches.