**Chapter Notes and Summary**

• **Length : **size of a line segment is its length, i.e., distance between two points of a line segment.•

**Units of measurement of Length :**

1 km = 1000 m

**1 m = 100 cm**

**1 dm = 10 cm**

**1 cm = 10 mm**

**1 foot = 12 inches**

**1 yard = 3 feet**

**•**

**Closed curve :**A curve having same beginning and ending point is called a closed curve.

**•**

**Simple curve :**A curve is a simple curve if it does not cross itself.

**•**

**Simple closed :**A curve having same beginning and ending point and which does not cross itself is called

**closed curve.**

**•**

**Interior region :**portion of plane inside curve, or bounded by curve, is called interior region.

**•**

**Exterior region :**portion of plane outside curve , is called exterior region.

**•**

**Perimeter of a plane figure :**sum of lengths of all sides of a plane figure, or length of its boundary, is

**called perimeter of figure.**

**•**

**Perimeter of a rectangle :**Perimeter of a rectangle = AB + BC + CD + DA

**= l + b + l + b = 2l + 2b**

**= 2(length + breadth) [Q opposite sides are equal]**

**= 2(l + b) units.**

**•**

**Perimeter of a square :**Perimeter of a square

**= AB + BC + CD + DA**

**= a + a + a + a**

**= 4 × side = 4a units, [Q all sides are equal]**

**•**

**Perimeter of a triangle :**Perimeter of a triangle is sum of all sides of any types of a triangle i.e., perimeter of

**ΔABC = AB + BC + AC.**

**(i) (ii)**

**•**

**For equilateral triangle :**Perimeter = AB + BC + AC = a + a + a + a = 3 × side.

**•**

**Circumference of a circle :**perimeter of a circle is called its circumference. length of thread that binds

**around circle exactly once gives circumference of circle.**

**•**

**An important result :**ratio of circumference of a circle and its diameter is always constant.

**•**

**Circumference =**2πr units, where r is radius of circle and

**Area of circle**= πr2.

**•**

**Area :**measurement of region enclosed by a plane figure is called area of figure.

**•**

**Area of a square =**(side)2 sq. units.

**•**

**Perimeter of a regular pentagon =**5 × length of a side.

**•**

**Perimeter of a regular hexagon =**6 × length of a side.

**•**

**Area of a right triangle =**1/2

**× base × height =**

**1/2**

**× b × h.**

**•**

**Area of an equilateral triangle =**3

**/**4

**× (side)2.**

**•**

**Standard unit of area :**We say that area of a square of side 1 cm is 1 square centimeter, written as 1 cm2. standard unit of area is cm2.

**• If a figure contains n squares, each of side 1 cm, we say that area of figure is n cm2.**

Note :

Note :