Quadrilaterals PowerPoint
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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