QUADRILATERAL(Segiempat)

Base of Competence

1. Identify the properties of rectangle, square, parallelogram, rhombus, kite and trapezoid.

2. Determine the perimeter and the area of quadrilateral and how to use it in problem solving

3. Solving of problem which has relation with perimeter and area of quadrilateral

4 vertices

A.

B.

C.

D.

• 4 sides• 4 angles

QUADRILATERALS(General Properties)

A.

B.

C.

D.

360o

The sum of ALL the angles of a

quadrilateral is 360oC

.

A.

D.

B.

QUADRILATERALS(General Properties)

A.

B.

C.

D.

360o

The sum of ALL the angles of a

quadrilateral is 360o

QUADRILATERALS(General Properties)

QUADRILATERALS(FOUR SIDED POLYGON)

6

RECTANGLE

PARALLELOGRAM

RHOMBUS

ISOSCELESTRAPEZOID

SQUARE

TRAPEZOID

CLASSIFICATIONOF

QUADRILATERAL

7

1. RECTANGLE

1

4

2

3

5

6

RECTANGLE IN OUR SUROUNDING

1. Has two pairs of parallel sides.

(AB // DC; AD // BC)

AB and DC; AD and BC are pairs of

opposite sides

2. Has two pairs of congruent sides.

5. All diagonals bisect each other

6. Opposite angles are congruent.

7. Consecutive angles are supplementary.

A B+ =180°

B C+ =180°

C D+ =180°

D A+ =180°

A

D

B

C 4. All diagonals are congruent

3. All angles are right angle.

THE PROPERTIES RECTANGLE

8. Has two axis of simmetry

9. Has rotational simmetry order 2

10. Can fits its frame in 4 ways

7x+3

9x – 13

In a rectangle diagonals bisect each other, then:

7x+ 3 = 9x – 13 3+13 = 9x – 7x16 =

2xx=8

R S

TU

RSTU is a RectangleRQ =7x + 3QT = 9x – 13

Find the value for x and QS.

Since all four segments formed when the diagonals bisect are congruent, finding one we’ll know the value for all.

RQ = 7x + 3 = 7( )

+ 38

= 56 + 3= 59

Q

The length of QS is 59.

RQ = TQ = QS = UQ

3x+5

6x – 10

In a rectangle diagonals bisect each other, then:

3x + 5 = 6x – 105 + 10 = 6x – 3x 15 =

3xx=5

A B

CD

ABCD is a RectangleBQ =3x + 5CQ = 6x – 10

Find the value for x and DQ.

Since all four segments formed when the diagonals bisect are congruent, finding one we’ll know the value for all.

BQ = 3x + 5 =3( ) +

55

= 15 + 5= 20

Q

The length of DQ is 20.

BQ = DQ = AQ = CQ

PERIMETER AND AREA

Perimeter of a shape is the total length of its sides.

Perimeter of a rectangle

length

width

length

width

= length + width + length + width

P = l + w + l + w

P = 2l + 2w

P = 2(l + w)

Perimeter

Area

Area measures the surface of something.

1 metre

1 metre

1 square metre

1m2

1 cm

1 cm 1cm2

1 mm

1 mm 1mm2

Area of a rectangular lawn

15 square metres

The area is

5 metres long

3 metres wide

Area of a rectangle

= Length x Width

= 15 m2

Example

1. The length and the width of a rectangle is enlarge 3 times. Find the ratio of:a. Original area to new areab. Original perimeter to new perimeter

2. The length of a rectangle is enlarge 2 times and the width is enlarge 3 times. Find the ratio of original area to new area.

3. The length of a rectangle is enlarge 2 times and the width is decrease ½ than original width. Find the ratio of original area to new area. (1 : 2 x ½ ) = (1 : 1)

4. The length of a rectangle is decreased 1/3 times and the length is enlarge 6 times. Find the ration of original area to new area. ( 1 : 1/3 x 6) = 1 : 2

5. The length of rectangle is changed to 1/3 than the original and the width is changed to ½ than the orginal. The ratio of original area to new area is ...( 1 : 1/3 x ½ = 1 : 1/6 = 6 : 1)

21

22

23

Example1. The length and the width of rectangle are

15 cm and 12 cm respectively. Find the perimeter and the area of rectangle.

2. The ratio of rectangle’s length and width is 5 : 3, if the perimeter of the rectangle is 64 cm find the length and the width of the rectangle.

3. The perimeter of rectangle is 80 cm. If the length is 4 cm more than the width, find the length and the width of the rectangle.

Example4. The area of the rectangle is 420 cm2. If the

length is 21 cm find the length of its diagonal.

5. The perimeter of a rectangle is 44 cm. The difference of its length and width is 6 cm. Find the area of the rectangle.

6. The ratio of rectangle’s length and width is 7 : 5, if the area of the rectangle is 315 cm2, then find the perimeter of the rectangle.

7. The length of the rectangle enlarge 5 times and the width is enlarge 3 times. The ratio of original area to new area is ....

26

1. Two pairs of parallel sides. AB//DC, AD// BC

2. All sides are congruent.

5. Diagonals intersect and bisect each other

7. Opposite angles are congruent.

8. Consecutive angles are supplementary.

A B+ =180°

B C+ =180°

C D+ =180°

D A+ =180°

A

D

B

C

4. Diagonals are congruent

3. All angles are right.

6. Diagonals are perpendicular

SQUARE

9. It has 4 axis simmetry

10. It has rational simmetry order 4

11. It can fits its frame in 8 ways

27

CHECK UNDERSTANDING

28

OLM

UV = .....

VX = .....

29

30

1. Look at the figures on the right. If the area of the square is equal to the area of the rectangle, then the perimeter of the rectangle is ....a. 20 cmb. 32 cmc. 40 cmd. 64 cm 

2. The perimeter of a rectangle is 38 cm. If the difference of the length and the width is 5 cm, then the length of the rectangle is ....a. 12 cmb. 10 cmc. 9 cmd.7 cm

8 cm

(3x-2) cm

4 cm

A B

CD

ABCD is a square.If BD = 12 cm, find the area of square ABCD

Problem Solving 1

Mr Ahmad has a rectangular pool with the measure of 20 m x 10 m. Around the outside of the pool will make a path with the width of 1 m.The path will wraped with ceramics. If the price of 1 m2 ceramics is Rp 60,000.00, how much money does Mr. Ahmad needs?

Problem Solving 1

Problem Solving 3

A B

CD

E

F

ABCD is a square.If AB = 6 cm and EF : BD = 1 : 3Then find the area of the shaded region. (EFC)

Problem Solving 4

PQRS is a rectangle.If PQ = 20 cm, QR = 15 cm and MN =½SQThen find the area of the shaded region. (PNRM)

P Q

RS

M

N