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

Parallelogram All angles are

90⁰

Parallelogram

All angles are 90⁰

All sides are equal in length

Rectangle Square 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 equalbase 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 ⁰B. 45 ⁰C. 65 ⁰D. 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 is measured in square unitsNumber of squares required to cover the

surface

Be 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 QUADRILATERALSType of Quadrilateral Area FormulaParallelogram A = bhRectangle A = bhSquare A = s²

Rhombus A = bhTrapezoid 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

A = (1/2)h(b1 + b2) = (1/2)(4)(9 + 6)

= (1/2)(60) = 30 cm ²

9cm

6cm

4cm

CLICKER QUESTION #3 What is the area of the parallelogram?

A. 50 cm²B. 60 cm²C. 17 cm²D. 22 cm²

CLICKER QUESTION #4 The area of a rhombus is 64 in² and

the base is 16 in. Find the height.

A. 4 in²B. 1024 inC. 80 in²D. 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 cm²B. 35 cm²C. 25 cm²D. 20 cm²

PAIRS #2 The area of a square is 169 square

feet. What is the length of each side?

A. 42.25 ftB. 84.5 ftC. 13 ftD. 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 inC. 448 in² D. 7 in

PAIRS #4 Find the missing angle:

A. 45⁰B. 65⁰C. 95⁰D. 115⁰

115⁰

x

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) A. 55 yd² B. 49 yd² C. 195 yd² D. 189 yd²

yard

sandbox

ANSWER #1

What is the measure of the missing angle?A. 115 ⁰B. 45 ⁰C. 65 ⁰D. 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 cm²B. 60 cm²C. 17 cm²D. 22 cm²

ANSWER #4 The area of a rhombus is 64 in² and

the base is 16 in. Find the height.

A. 4 in²B. 1024 inC. 80 in²D. 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 cm²B. 35 cm²C. 25 cm²D. 20 cm²

PAIRS – ANSWER #2 The area of a square is 169 square

feet. What is the length of each side?

A. 42.25 ftB. 84.5 ftC. 13 ftD. 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 inC. 448 in² D. 7 in

PAIRS – ANSWER #4 Find the missing angle:

A. 45⁰B. 65⁰C. 95⁰D. 115⁰

115⁰

x

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) A. 55 yd² B. 49 yd² C. 195 yd² D. 189 yd²

yard

sandbox