Lesson 30-3: Areas of Rhombuses, Kites,
and Trapezoids
We will derive the formulas for the area
of rhombuses, kites, and trapezoids
and
I will solve problems using the areas of
rhombuses, kites, trapezoids, and
composite figures.
March 29, 2017
Finding the formula for area of a
Rhombus
1. Draw a rhombus by first carefully constructing two
lines that are  bisectors. Label them d1 and d2.
2. Connect the ends of those two lines to form a
rhombus.
3. Measure the sides to make sure it is correct.
Finding the area of a Rhombus
d1/2
d2/2
1. The rhombus can be divided into 2 triangles by the
diagonals. (d1 & d2).
2. Find the area of one of the triangles:
A =½ bh
b= d1 h= ½d2
1 d2 d1d2
A  d1

2 2
4
3. The rhombus is 2 of these triangles, so area of
the rhombus is:
dd
dd
A2
1 2
4

1 2
2
Area of a Rhombus or Kite – half the product
of the 2 diagonals. –
Adiagonals
d1  d2

2
d1/2
d2/2
Example: Find the area and perimeter of the
rhombus.
d1d2
A
2
5
24  10
A
5
2
12
A  120
P  4  13  52
• On a top half of a piece of paper, draw a
trapezoid.
• Fold the paper in half and cut the trapezoid
out of both thicknesses to obtain 2
trapezoids.
• Piece them together to form a
parallelogram.
h
b1
b1
b2
h
b2
h
b2
b1
h
b1
b2
What is the area of the parallelogram?
A = (b1 + b2)h
How does the area of one trapezoid
compare to the area of the parallelogram?
one-half
What is the formula for the area of a
b
b
trapezoid?
1
(b1  b2 )h
2
h
2
h
b2
b1
Area of a Trapezoid
(b1  b2 )h
A
2
But…
(b1  b2 )
Midsegment of a Trapezoid 
2
So another way to calculate the area is
A = midsegment(height)
Example: Find the midsegment, area and
perimeter of the trapezoid.
b1  b2
midsegment 
2
26  12
midsegment 
2
A  (mids)(h)
A  19(9)
A  171
38
midsegment 
2
midsegment  19
Example: Find the midsegment, area and
perimeter of the trapezoid.
9
sin 46 
x
12.51
9
sin 60 
x
9
x
sin 60
x  10.39
9
10.39
9
x
sin 46
x  12.51
P  12  12.51  26  10.39
P  60.9