all formulas of chapter mensuration class 8 ncert
Answers
Answer:
By constructing EC || AB, we can split the given figure (AEDCBA) into two parts (Triangle ECD right-angled at C and Rectangle AECB), Here, b = a + c = 30 m
Mensuration Class 8
Now, Area of Triangle DCE:
1/2 × CD × EC= 1/2 × c × s
h = 1/2 ×10× 12 = 60 m2
Also, Area of rectangle AECB = AB × BC = h × a=12 × 20=240 m2
Therefore, Area of trapezium AEDB = Area of Triangle DCE + Area of rectangle AECB = 60 + 240 = 300 =300m2
Area of quadrilateral ABCD
Mensuration Class 8
Diagonal AC divides the given quadrilateral into two triangles i.e. Triangle ABC and Triangle ADC.
Now, Area of Quadrilateral ABCD = Area of Triangle ABC + Area of Triangle ADC.
=1/2 × AC × h1 + 1/2 × AC × h2 =1/2 × d × (h1 +h2)
Where, d = The length of diagonal of a quadrilateral.
Mensuration Class 8 Formulas and Notes
The important formulas covered in this chapter are as follows:
Area of Trapezium height x (sum of parallel sides)/2
Area of Rhombus ½ x d1 x d2
Area of Special Quadrilateral ½ x d x (h1 + h2)
Surface area of Cuboid 2(lb x bh x hl)
Surface area of Cube 6a2
Surface area of cylinder 2πr(r + h)
Volume of Cuboid l × b × h
Volume of Cube a3
Volume of cylinder πr2h
Where,
d1 and d2 are the diagonals of the rhombus
d is the diagonal of a special quadrilateral which is divided into two triangles
h1 and h2 are the two perpendiculars from the vertices of a quadrilateral to its diagonal
l, b and h denotes length, breadth and height of the cuboid
r represents the radius of the cylindrical base
a is the side of the cube
Note:
The trapezium and rhombus are the figures represented in the two-dimensional plane. Whereas Cuboid, Cube and Cylinder are three-dimensional solid shape.
The surface area of a solid shape is the sum of the areas of its faces.
Amount of region occupied by a solid shape is called its volume.
Answer:
surface area of :
a cuboid=2(lb+bh+hl)
a cube=6lsquare
a cylinder=2πr(r+h)
volume of :
a cuboid=l×b×h
a cube =l cube
a cylinder=πr square h