Rhombus A parallelogram with opposite equal acute and obtuse angles and four equal sides.
Diagonals
Diagonals
4 equal sides
Area of a Rhombus
Same as Area of parallelogram
A = b . h
b
h
Special “Rhombus Rule”Since the diagonals are perpendicularAnother way to find the area of a rhombus is:Area = ½ (product of the diagonals)
d 1
d2
area = ½ (d1 . d2)
This is good when you only know the diagonals, but not the sides or height
Area of a Rhombus
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) = 6Area of 4 triangles = 4(6) = 24Notice that 1/2d1d2 or ½(6)(8), also equals 24
The formula for the area of a rhombus can be justified using the area of a triangle. A specific case follows.
Find the Area of a RhombusExample 3
Find the area of the rhombus.a. b.
= 108The area of the rhombus is 70 square inches.
The area of the rhombus is 108 square inches.
SOLUTION
A = d1d221a.
SOLUTION
b. A = d1d221
21 (14)(10)= (6 + 6)(9 + 9)= 2
1
= 70 (12)(18)= 21