# OP Malhotra Area Theorems Class-9 S.Chand ICSE Maths Ch-12

OP Malhotra **Area Theorems** Class-9 S.Chand ICSE Maths Ch-12. We Provide Step by Step Answer of Exe-12 of S Chand OP Malhotra Maths . Visit official Website CISCE for detail information about ICSE Board Class-9.

## OP Malhotra Area Theorems Class-9 S.Chand ICSE Maths Ch-12

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Exercise-12

### OP Malhotra Area Theorems Class-9 S.Chand ICSE Maths Ch-12

**Area Theorems :**

**Theorem 1**

Parallelograms on the same base and between the same parallels are equal in area. Area of (||gm ABCE) = Area of (||gm ABDF) as they lie on the same base AB and AB||DF.

**Theorem 2**

The area of a parallelogram is equal to the area of the rectangle on the same base and of the same altitude, i.e., between the same parallels.

Area of (||gm ABCD) = Area of (rectangle ABEF) as they lie on the same base AB

and between the same parallels AB and DE

**Theorem 3**

The area of a triangle is half of that of a parallelogram on the same base and between the same parallels.

Area of (∆ APB) = 1/2 × Area of (||gm ABCD) as they lie on the same base AB

and between the same parallels AB and PC.

**Theorem 4**

Triangles on the same base and between the same parallels are equal in area. Area of (∆ ABD) = Area of (∆ ABC) as they lie on the base AB and between the same parallels AB and DC.

#### A**rea Axioms:**

Every polygonal region R has an area, measure in square unit and denoted by ar(R).

(i) **Congruent area axiom** :if R1 and R2 be two regions such that R1∼R2 then ar(R1) = ar (R2).

(ii)** Area monotone axiom** :If R1⊂ R2, then are (R1) <ar(R2).

(iii**) Area addition axiom** :If R1 are two polygonal regions, whose intersection is a finite number of points and line segments and R = R1υ R2, then ar (R) = ar(R1) + ar(R2).

(iv**) Rectangular area axiom :**If AB = a metre and AD = b metre then, ar (Rectangular region ABCD) = ab sq. m.

**Unit of Area :**

There is a standard square region of side 1 metre, called a square metre, which is the unit of area measure. The area of a polygonal region is square metres (sq. m or m2) is a positive real number

### Exercise-12

OP Malhotra Area Theorems Class-9 S.Chand ICSE Maths Ch-12

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