QUADRILATERAL (Segiempat)

Base of Competence Identify the properties of rectangle, square, parallelogram, rhombus, kite and trapezoid. Determine the perimeter and the area of quadrilateral and how to use it in problem solving Solving of problem which has relation with perimeter and area of quadrilateral

QUADRILATERALS (General Properties) 4 vertices B . 4 sides 4 angles A . D . C .

QUADRILATERALS (General Properties) . B C D 360o C . A D B The sum of ALL the angles of a quadrilateral is 360o

The sum of ALL the angles of a quadrilateral is 360o QUADRILATERALS (General Properties) A . B C D 360o The sum of ALL the angles of a quadrilateral is 360o

QUADRILATERALS (FOUR SIDED POLYGON) CLASSIFICATION OF QUADRILATERAL PARALLELOGRAM RHOMBUS SQUARE RECTANGLE TRAPEZOID ISOSCELES TRAPEZOID

1. RECTANGLE Which is rectangle ? 1 3 2 4 5 6

RECTANGLE IN OUR SUROUNDING

THE PROPERTIES RECTANGLE Has two pairs of parallel sides. (AB // DC; AD // BC) AB and DC; AD and BC are pairs of opposite sides THE PROPERTIES RECTANGLE A B 2. Has two pairs of congruent sides. 3. All angles are right angle. D C 4. All diagonals are congruent 5. All diagonals bisect each other 8. Has two axis of simmetry 6. Opposite angles are congruent. 9. Has rotational simmetry order 2 7. Consecutive angles are supplementary. A B + = 180° C D 10. Can fits its frame in 4 ways

R S RSTU is a Rectangle 7x+3 RQ =7x + 3 Q 9x – 13 QT = 9x – 13 Find the value for x and QS. U T In a rectangle diagonals bisect each other, then: Since all four segments formed when the diagonals bisect are congruent, finding one we’ll know the value for all. 7x+ 3 = 9x – 13 RQ = 7x + 3 3+13 = 9x – 7x = 7( ) + 3 8 16 = 2x = 56 + 3 x=8 = 59 RQ = TQ = QS = UQ The length of QS is 59.

A B ABCD is a Rectangle 3x+5 BQ =3x + 5 Q CQ = 6x – 10 6x – 10 Find the value for x and DQ. D C In a rectangle diagonals bisect each other, then: Since all four segments formed when the diagonals bisect are congruent, finding one we’ll know the value for all. 3x + 5 = 6x – 10 BQ = 3x + 5 5 + 10 = 6x – 3x =3( ) + 5 5 15 = 3x = 15 + 5 x=5 = 20 BQ = DQ = AQ = CQ The length of DQ is 20.

PERIMETER AND AREA Perimeter Perimeter of a shape is the total length of its sides. Perimeter of a rectangle = length + width + length + width length width width P = l + w + l + w P = 2l + 2w length P = 2(l + w)

Area Area measures the surface of something. 1 metre 1 cm 1 mm 1 metre 1 square metre

Area of a rectangular lawn 5 metres long 3 metres wide The area is 15 square metres = 15 m2 Area of a rectangle = Length x Width

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

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) 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 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)

Example The length and the width of rectangle are 15 cm and 12 cm respectively. Find the perimeter and the area of rectangle. 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. 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.

Example 4. The area of the rectangle is 420 cm2. If the length is 21 cm find the length of its diagonal. The perimeter of a rectangle is 44 cm. The difference of its length and width is 6 cm. Find the area of the rectangle. 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. The length of the rectangle enlarge 5 times and the width is enlarge 3 times. The ratio of original area to new area is ....

SQUARE 1. Two pairs of parallel sides. AB//DC, AD// BC A B 2. All sides are congruent. 3. All angles are right. 4. Diagonals are congruent 5. Diagonals intersect and bisect each other D C 6. Diagonals are perpendicular 9. It has 4 axis simmetry 7. Opposite angles are congruent. 10. It has rational simmetry order 4 8. Consecutive angles are supplementary. A B + = 180° C D 11. It can fits its frame in 8 ways

CHECK UNDERSTANDING

OLM UV = ..... VX = .....

1. Look at the figures on the right 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 cm b. 32 cm c. 40 cm d. 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 cm b. 10 cm c. 9 cm d.7 cm 8 cm (3x-2) cm 4 cm

Problem Solving 1 ABCD is a square. If BD = 12 cm, find the area of square ABCD A B

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

Problem Solving 4 PQRS is a rectangle. If PQ = 20 cm, QR = 15 cm and MN =½SQ Then find the area of the shaded region. (PNRM)