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