# 6 Math Chapter 10 Mensuration

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