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**11. Perimeter and Area**

**Plane Figures**

The area of the parallelogram is given by base** x height.**

**Triangle:**

A **triangle is a polygon with three vertices**, and** three sides **or edges that are line segments. A triangle with vertices A, B, and C is denoted as ABC

The** perimeter of a triangle **is the sum of the lengths of its sides. If the three sides are a, b, and c, then perimeter

**Page 43**

The** area of a triangle** is the space enclosed by its three sides. It is given by the formula, where b is the base and h is the altitude.

A simple** closed figure bounded** by** four line segments i**s called a **quadrilateral.**

**Various types of quadrilateral are:****â€¢** Rectangle**â€¢** Square**â€¢** Parallelogram**â€¢** Rhombus

A **rectangle is a quadrilateral** with opposite sides equal, and each angle of measure 90o.

**Page 44**

The **perimeter of a rectangle** is twice the sum of the lengths of its adjacent sides.

In the figure, the perimeter of rectangle ABCD = 2(AB + BC).

The** area of a rectangle **is the product of its length and breadth.

In the figure, the area of rectangle ABCD = AB x BC.

A square is a** quadrilateral with four equal sides**, and each angle of measure 90o.

The **perimeter of a square **with side s units is 4s.

In the figure, the perimeter of square ABCD = 4AB or 4BC or 4CD or 4DA.

The area of a **square **with side s is s^{2}

In the figure, the perimeter of square ABCD = AB^{2} or BC^{2} or CD^{2} or DA^{2}.

**Page 45**

A **quadrilateral** in which both the pairs of opposite sides are parallel is called a parallelogram.

The** perimeter of a parallelogram** is twice the sum of the lengths of the adjacent sides.

In the figure, the perimeter of parallelogram ABCD = 2(AB + BC)

The **area of a parallelogram **is the product of its **base and perpendicular height or altitude.**

Any side of a parallelogram can be taken as the base. The perpendicular dropped on that side from the opposite vertex is known as the **height (altitude).**

In the figure, the area of parallelogram ABCD = AB x DE or AD x BF.

A **parallelogram** in which the adjacent sides are equal is **called a rhombus.**

The perimeter and area of a rhombus can be calculated using the same formulae as that for a parallelogram.

**Page 46**

**Circles**

A circle is defined as a collection of points on a plane that are at an equal distance...

**Circle:**

A circle is defined as a collection of points on a plane that are at an equal distance from a fixed point on the plane. The fixed point is called the** centre of the circle.**

**Circumference:**

The distance around a circular region is known as its circumference.

**Diameter:**

Any straight line segment that passes through the centre of a circle and whose end points are on the circle is called its diameter.

**Radius:**

Any line segment from the centre of the circle to its circumference.

**Page 47**

Circumference of a circle = 2Ï€r, where r is the radius of the circle or , where Ï€d is the diameter of the circle.

Î is an irrational number, whose value is approximately equal to .

Circumference = Diameter x 3.14

Diameter(d) is equal to twice radius(r). **d=2r**

Circles with the same** centre** but different radii are called** concentric circles.**

**Circle:**

The **area** of a circle is the region enclosed in the circle.

The **area of a circle** can be calculated by using the formula:

**â€¢** if radius r is given**â€¢** if diameter D is given**â€¢** if circumference C is given

210 videos|109 docs|45 tests

### NCERT Solutions(Part - 3) - Perimeter and Area

- Doc | 7 pages
### Understanding: Area of Squares and Rectangle

- Video | 03:37 min
### Test: Perimeter And Area - 2

- Test | 20 ques | 20 min
### Area of a Triangle

- Video | 05:30 min
### Test: Perimeter And Area - 3

- Test | 20 ques | 20 min
### Examples: Perimeter and Area of Square and Rectangle

- Video | 06:00 min

- NCERT Solutions(Part - 2) - Perimeter and Area
- Doc | 6 pages
- Test: Perimeter And Area - 1
- Test | 16 ques | 10 min