PROPERTIES OF
QUADRILATERALS
QUADRILATERALS
 Two-dimensional,
closed shape
 Four straight sides
and four angles
 Sum of angles: 360⁰
 Diagonals AC, BD

Line segment from
one vertex to the
opposite vertex
 Seven
types of
quadrilaterals
PARALLELOGRAM
 Opposite
sides are parallel & equal
 Opposite angles are
equal
TYPES OF PARALLELOGRAMS
Rectangle
Parallelogram
 All angles are
90⁰

Square
Parallelogram
 All angles are
90⁰
 All sides are
equal in
length

Rhombus



Parallelogram
Opposite angles
are equal, do not
have to be 90⁰
All sides are
equal in length
TRAPEZOID
 One
pair of
opposite sides are
parallel
 A “regular”
trapezoid:
non-parallel sides
ARE equal
 base angles are
equal

Regular trapezoid
http://www.math.com/school/subject3/lessons/S3U2L3DP.html
OTHER QUADRILATERALS
 Irregular

quadrilaterals
No specifications
 Kite
Two pairs of adjacent sides are equal in length
 One pair of opposite angles (the ones that are
between the sides of unequal length) are equal
in size.
 One diagonal bisects the other.
 Diagonals intersect at
right angles.

CLICKER QUESTION #1
 What
is the
measure of the
missing angle?




A. 115 ⁰
B. 45 ⁰
C. 65 ⁰
D. 125 ⁰
115⁰
65 ⁰
X
115 ⁰
CLICKER QUESTION #2
 Which
of the following is not true?
A. The diagonals of a rhombus are congruent.
 B. The diagonals of a rectangle are congruent.
 C. The four sides of a rhombus are congruent.
 D. The rectangle has 4 right angles.
 E. A rhombus is a parallelogram.

AREA OF QUADRILATERALS
 Area

Number of squares required to cover the surface
 Be

is measured in square units
consistent with units
Example: If a rectangle is 6 inches wide and 4
feet long, what is the area?

Solution: Must convert units to make both
measurements consistent. 6 inches = ½ feet
 ½ ft x 4 ft = 2 ft²
 Area = 2 ft²
AREA OF QUADRILATERALS
Type of Quadrilateral
Area Formula
Parallelogram
A = bh
Rectangle
A = bh
Square
A = s²
Rhombus
A = bh
Trapezoid
A = (1/2)h(b1 + b2)
Kite
A = (1/2)(d1*d2)
Irregular
Break into parts & add
Key:
b – base
h – height
s – side
b1/b2 – base1/base2
d1/d2 – diagonal1/diagonal2
EXAMPLE - FIND AREA OF QUADRILATERAL
6cm

4cm
9cm
A = (1/2)h(b1 + b2)
= (1/2)(4)(9 + 6)
= (1/2)(60)
= 30 cm ²
CLICKER QUESTION #3
 What




is the area of the parallelogram?
A. 50 cm²
B. 60 cm²
C. 17 cm²
D. 22 cm²
CLICKER QUESTION #4
 The
area of a rhombus is 64 in² and the
base is 16 in. Find the height.

A. 4 in²

B. 1024 in

C. 80 in²

D. 4 in
COMPLETE WORKSHEET IN PAIRS
PAIRS #1
A
quadrilateral has four sides of equal
length and the diagonals are not
congruent. Each side is 5 cm in length
and the distance between parallel sides is
7 cm. Determine what type of
quadrilateral this is and use the
corresponding formula to find the area.




A. 12 cm²
B. 35 cm²
C. 25 cm²
D. 20 cm²
PAIRS #2
 The
area of a square is 169 square feet.
What is the length of each side?
A. 42.25 ft
 B. 84.5 ft
 C. 13 ft
 D. 14 ft

PAIRS #3
 The
area of a rectangle is 56 in² and the
base is 8 in. Find the height.
A. 8 in²
 B. 448 in
 C. 448 in²
 D. 7 in

PAIRS #4
 Find
the missing angle:
115⁰
x




A. 45⁰
B. 65⁰
C. 95⁰
D. 115⁰
PAIRS #5

The Smith family has a rectangular backyard
with a base of 18 yards and a height of 11 yards.
They want to put new grass in the whole
backyard; however, there is a square sandbox
with sides of 3 yards each in the yard. How
many square yards of new grass will they need?
(hint: they do not need grass to cover the
sandbox)
yard
A. 55 yd²
 B. 49 yd²
 C. 195 yd²
 D. 189 yd²

sandbox
ANSWER #1
 What
is the measure of the missing angle?
A. 115 ⁰
 B. 45 ⁰
 C. 65 ⁰
 D. 125 ⁰


What method did you use to solve for the answer?
ANSWER #2
 Which
of the following is not true?
A. The diagonals of a rhombus are congruent.
 B. The diagonals of a rectangle are congruent.
 C. The four sides of a rhombus are congruent.
 D. The rectangle has 4 right angles.
 E. A rhombus is a parallelogram.

ANSWER #3
 What




is the area of the parallelogram?
A. 50 cm²
B. 60 cm²
C. 17 cm²
D. 22 cm²
ANSWER #4
 The
area of a rhombus is 64 in² and the
base is 16 in. Find the height.

A. 4 in²

B. 1024 in

C. 80 in²

D. 4 in
PAIRS – ANSWER #1
A
quadrilateral has four sides of equal
length and the diagonals are not
congruent. Each side is 5 cm in length
and the distance between parallel sides is
7 cm. Determine what type of
quadrilateral this is and use the
corresponding formula to find the area.




A. 12 cm²
B. 35 cm²
C. 25 cm²
D. 20 cm²
PAIRS – ANSWER #2
 The
area of a square is 169 square feet.
What is the length of each side?
A. 42.25 ft
 B. 84.5 ft
 C. 13 ft
 D. 14 ft

PAIRS – ANSWER #3
 The
area of a rectangle is 56 in² and the
base is 8 in. Find the height.
A. 8 in²
 B. 448 in
 C. 448 in²
 D. 7 in

PAIRS – ANSWER #4
 Find
the missing angle:
115⁰
x




A. 45⁰
B. 65⁰
C. 95⁰
D. 115⁰
PAIRS – ANSWER #5

The Smith family has a rectangular backyard
with a base of 18 yards and a height of 11 yards.
They want to put new grass in the whole
backyard; however, there is a square sandbox
with sides of 3 yards each in the yard. How
many square yards of new grass will they need?
(hint: they do not need grass to cover the
sandbox)
yard
A. 55 yd²
 B. 49 yd²
 C. 195 yd²
 D. 189 yd²

sandbox