SUBJECT MATHEMATICS CLASS VIII TOPICAREA OF QUADRILATERALS TEXT

SUBJECT : MATHEMATICS CLASS : VIII TOPIC-AREA OF QUADRILATERALS

TEXT BOOK CHAPTER LINK: https: //drive. google. com/file/d/1 c. Irq 6 L 0 o. O 6 B 7 QDDHxi. GB 4 Cz. IMBEk. IIr/view? usp=sharing

LEARNING OBJECTIVE AT THE END OF THIS CHAPTER, STUDENTS WILL BE ABLE TO: ØIDENTIFY DIFFERENT TYPES OF QUADRILATERALS Ø EXPLORE PROPERTIES OF TRAPEZIUM AND ITS AREA Ø EXPLORE GENERAL QUADRILATERAL AND ITS AREA Ø EXPLORE DIFFERENT POLYGONS AND THEIR AREA

Can you see the quadrilaterals and all different polygons here………

Let’s Recall Rectangle Square Parallelogram Rhombus

Parallelogram height base A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Area of a parallelogram = base x height

RHOMBUS diagonal height base A parallelogram with all its sides equal is called a rhombus. Area of rhombus= base x height = ½ x (product of diagonals)

RECTANGLE breadth length Ø A quadrilateral with opposite sides equal and four right angles, or a parallelogram having all its angles as right angles Ø Area of a rectangle= length x breadth

SQUARE a unit A quadrilateral having all equal sides and all equal angles is a square. Area of a square = side x side = (a x a) square units

A Trapezium • A Trapezium is a quadrilateral in which one pair of opposite sides are parallel. • Here, ABCD is a Trapezium in which B A side AB is parallel to side CD and sides AC and BD are other two sides. h • The perpendicular distance between the parallel sides is known as the C D “height” of the Trapezium (h).

Examples of a Trapezium • Following figures are Trapeziums:

Area of a Trapezium • B A h C D

ACTIVITY(AREA OF A TRAPEZIUM) VIDEO LINK: https: //youtu. be/5 cr 0 x. CNSc. D 8

Special Trapezium – An Isosceles Trapezium • A Trapezium in which the non-parallel sides are equal in length is called an Isosceles Trapezium. B A • In an Isosceles Trapezium, the base angles (i. e. angle ACD and angle CDB in this case) and the vertex angles (i. e. angle CAB and angle ABD in this case) are equal. • Here, ABCD is an Isosceles Trapezium. C • Thus, the non parallel sides AC and BD are equal (AC = BD), the base angles are equal (angle ACD = angle BDC), the vertex angles are equal (angle CAB = angle DBA) D

Solved Example •

Solved Example •

Special Trapezium – A Parallelogram • If, in a Trapezium, the non-parallel sides also become parallel, it becomes a Parallelogram. • Here, ABCD is a Trapezium and PQRS is a Parallelogram. A C B P D R S Q

Solved Example • 13 cm A 15 cm F h 15 cm h E B D 13 cm 25 cm C

Cont…. . • 13 cm A 15 cm F h 15 cm h E B D 13 cm 25 cm C

A General Quadrilateral • When we say “A General Quadrilateral”, we mean a quadrilateral which does not necessarily have any special properties and thus isn’t called a Square/Rectangle/Rhombus/Parallelogram/Trapezium/Kite • It is just a closed plane figure bounded by 4 line segments. It has four sides and four interior angles, which add up to 360 degrees Q • PQRS given here is a General Quadrilateral P R S

Area of a General Quadrilateral • Q P R S

Area of a General Quadrilateral VIDEO LINK: https: //youtu. be/Y_jm 760 -5 A 0 (Explanation by teacher)

DERIVATION Q • P N M R S

Solved Example D • 4 cm 10 cm A 5 cm B C

Area of a Polygon •

For Example… • Area of Pentagon ABCDE here can be found by drawing a diagonal AD such that the whole Pentagon is now divided into a Rectangle ABCD and a Triangle ADE. E A D B • Thus, C Area of Pentagon ABCDE = Area of Rectangle ABCD + Area of Triangle ADE

Solved Example H • G 8 m A F 22 m 10 m B E 8 m C D

ART INTEGRATION

ACTIVITY (ART INTEGRATION) MY BARBIE Make any cartoon using different shapes of quadrilateral and polygons

In a Nutshell… Parallelogram = Base x Height Area of a Rectangle = length x breadth Square = (side)2 Polygon = Sum of areas of its constituent triangles and quadrilaterals

PROJECT (ART INTEGRATION) Prepare a trapezium shaped hand book on area of different quadrilaterals and polygons and their key points

WORKSHEETS

LEARNING OUTCOME Ø Realization of the fact that from the laptop key they are pressing to the monitor screen they are viewing, quadrilaterals are involved. The laptop which is in rectangular shape sitting on their squared shaped table requires rectangle shaped floor to stand. Pillars supporting floor and roof are not left with quadrilaterals not being involved. Ø Can use the concept of finding area of general quadrilateral and polygons and can correlate it with finding of area of a land property in daily life situation. Ø Can apply the concepts of quadrilaterals to estimate the no of tiles required for flooring, etc.