- Area of figure
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- Properties of Area
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- Figure on the same base and between same parallels
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- Parallelogram on same base and between same parallel
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- Area of Parallelogram
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- How to solve the Area problem
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- Triangles and Parallelogram
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- Area of Triangle
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- How the Parallelogram area is calculated

Area can be measured in various ways

1) Area by Counting Squares: We can also put the shape on a grid and count the number of squares of unit area

2) Approximate Area by Counting Squares: Sometimes the squares don't match the shape exactly, but we can get an "approximate" answer using more than half a square counts as 1 and less than half a square counts as 0

3) Using a formula (when possible) : It can be calculated using mathematics formula. We can find formula for various figures

4) Area of Difficult Shapes: We can sometimes break a shape up into two or more simpler shapes for which we know the formula

5) Area by Adding Up Triangles : We can try to divide the area into multiples traingle and then calculating the area

1) Area by Counting Squares: We can also put the shape on a grid and count the number of squares of unit area

2) Approximate Area by Counting Squares: Sometimes the squares don't match the shape exactly, but we can get an "approximate" answer using more than half a square counts as 1 and less than half a square counts as 0

3) Using a formula (when possible) : It can be calculated using mathematics formula. We can find formula for various figures

4) Area of Difficult Shapes: We can sometimes break a shape up into two or more simpler shapes for which we know the formula

5) Area by Adding Up Triangles : We can try to divide the area into multiples traingle and then calculating the area

Two figures are congruent, if they're exactly the same shape, and they're exactly the same size. They may appear different because one is shifted or rotated a certain way, but they're still the same shape, and all the sides of one are the same length as the corresponding sides of the other.

3) If a planar region formed by a figure T is made up of two non-overlapping planar regions

Formed by figures P and Q, then ar (T) = ar (P) + ar (Q), where ar (X) denotes the area of Figure X.

In the above figure triangle and parallelogram are on the same base and between same parallel

Parallelograms on the same base (or equal bases) and between the same parallels are equal in area.

Area of Parallelogram ABCD= Area of Parallelogram PBCQ

A parallelogram is a 4-sided shape formed by two pairs of parallel lines. Opposite sides are equal in length and opposite angles are equal in measure.

To find the area of a parallelogram, multiply the base by the height. The formula is:Area of parallelogram is equal base multiplied by Height

The base and height of a parallelogram must be perpendicular. However, the lateral sides of a parallelogram are not perpendicular to the base. Thus, a line is drawn to represent the height.

Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallel

2)Calculate the area using the formula

3) If the area is given and either height or base is missing,then we can find using b=A/h or h=A/b

1) Find the area of a parallelogram with a base of 2 inches and a height of 10 inches.

A = (2 in).(10 in)

A = 20 in

2)The area of a parallelogram is 12 square centimeters and the base is 4 centimeters. Find the height

Solution: Let h be the height then

12 = (4 ).h

h = 3 cm

a) If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of parallelogram

Area of triangle ADB= 1/2 X Area of parallelogram ABCD

b) Triangles on the same base (or equal bases) and between the same parallels are equal in area

Area of triangle ABD=Area of triangle ACB

A=1/2 BXH

2) Triangles on the same base (or equal bases) and having equal areas lie between the same

Parallels

A=L X B

Now let us consider the parallelogram given below

Here B is the Base of the parallelogram

and H is the height of the parallelogram

Let us move the traingle part as shown in figure to the other side

Which is a rectangle of Area =BH

Given below are the links of some of the reference books for class 9 Math.

- Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
- Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
- Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
- Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.

Class 9 Maths Class 9 Science

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