AP Board Class 9 Maths Chapter 11 Areas

AP Board Class 9 Maths Chapter 11 which covers the topic of areas has been designed to help students learn how to calculate the areas of triangles, squares, rectangles and quadrilaterals by using some formulae.  In this unit, they will also explore the basis of these formulae and discuss how are they derived.

What is Area?

In simple terms, the area of a shape or a figure is a measurement of how much space is available on a flat surface or how much plane is enclosed by a certain figure. As there are several types of shapes there are different ways to find the area for each shape. Area is measured in square units.

Areas of Shapes and Their Formulas

The area of shapes can be found using some of the formulas given below;

AP Board Class 9 Maths Chapter 11 Areas
AP Board Class 9 Maths Chapter 11 Areas
AP Board Class 9 Maths Chapter 11 Areas

Students can check out some of the chapter questions along with their solutions to know more about the concept.

Question 1: Show that the diagonals of a parallelogram divide it into four triangles of equal area.

    Solution:

    Consider a parallelogram ABCD as shown below

    AP Board Class 9 Maths Chapter 11 Areas

    As seen, the diagonals BD and CA bisect each otherat the point O.

    O is the midpoint of BD, hence OD = OB

    Similarly, O is the midpoint of AC, hence OC = OA

    In △ ABC,

    As OC = OA, OB is the median of △ ABC,

    Therefore, the area of △ BOA = the area of △ BOC……..(1)

    In △ ADC,

    As OC = OA, OD is the median of △ ADC

    Therefore, the area of △ DOA = the area of △ DOC……….(2)

    Median divides the triangle into two equal areas

    Similarly, in △ ADB since OD = OB, OA is the median

    Hence, the area of △ AOB = the area of △ AOD…………….(3)

    From (1), (2) and (3) we can conclude that the diagonals of a parallelogram divide it into four triangles of equal area

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Practise This Question

ABCD is a quadrilateral as shown below. AD=AB and CB=CD.

What can be said about quadilateral ABCD?