Introduction
Triangular pyramid how many faces a pyramid is a solid three dimensional shape formed by connecting the base which can be any polygon and the apex . Pyramids have a base which is a polygon with ' n ' sides then the number of faces it has will be equal to ' n '. If the number of faces is ' n ' then the number of vertices will be ' n + 1 ' and the number of edges are ' 2n ' . Pyramids are specified according to their base shape , if it is unspecified then it is normally assumed the pyramid has a square base .
Triangular pyramid means it has a triangle base , when a pyramid is made up of four equilateral triangles then it is called a tetrahedron . A tetrahedron has four equilateral triangular faces (any one of the face can be considered as a base) , four vertices's and six edges . In a tetrahedron all angles and all edges are equal .
Triangular Pyramid How many Faces : Surface Area and Volume.
Triangular pyramid how many faces? A triangular pyramid has 3 faces and one base , we can say it has all together 4 faces as we see a Tetrahedron has 4 faces each one is an equilateral triangle so any face may be considered as the base .
Surface Area
The surface area of a triangular pyramid is given by...
S.A = Area of base + 3 ( Area of a face ) = 1/2 s a + 3 ( 1/2 s l )
S.A = 1/2 x s a + 3/2 s l sq.units. where ' a ' is the height of base triangle , ' s ' is the side length of the base triangle which is again the base of the face triangle , ' l ' is the slant height or the height of the face triangle .
For a tetrahedron surface area S.A = 4 ( 1/2 s a ) = 2 s a , where ' s ' is the base of any face and ' a ' is the height or slant height .
Volume
Volume of a triangular pyramid is given by...
V = 1/3 times Area of base triangle times height of the pyramid .
V = 1/3 x ( 1/2 s a ) h = 1/6 s a h cubic units
Triangular Pyramid How many Faces:example Problems
Ex 1: Find the surface area and volume of the given triangular pyramid .
Sol : Surface area S.A = area of base + area of three faces ( s = 6 cm , a = 4 cm , l = 8 cm , h = 5 cm )
area of base = 1/2 sa = 1/2 x 6 x 4 = 12 cm2, area of three faces = 3/2 (sl) = 3/2 ( 6 x 8 ) = 3 ( 24 ) = 72 cm2
Therefore S.A = 12 cm + 72 cm = 842 cm
Volume V = 1/6 sah = 1/6 x 6 x 4 x 5 = 20 cm3
Ex 2 : The surface area of a tetrahedron is 112 m2 , find the area of the base.
Sol: A tetrahedron has four congruent faces , the area of all four faces are equal and any face can be considered as base.
So , The area of the base in the given tetrahedron = 112/4 = 28 m2 .
Algebra is widely used in day to day activities watch out for my forthcoming posts on polynomials and factoring and factoring polynomials degree 3. I am sure they will be helpful.
Triangular pyramid how many faces a pyramid is a solid three dimensional shape formed by connecting the base which can be any polygon and the apex . Pyramids have a base which is a polygon with ' n ' sides then the number of faces it has will be equal to ' n '. If the number of faces is ' n ' then the number of vertices will be ' n + 1 ' and the number of edges are ' 2n ' . Pyramids are specified according to their base shape , if it is unspecified then it is normally assumed the pyramid has a square base .
Triangular pyramid means it has a triangle base , when a pyramid is made up of four equilateral triangles then it is called a tetrahedron . A tetrahedron has four equilateral triangular faces (any one of the face can be considered as a base) , four vertices's and six edges . In a tetrahedron all angles and all edges are equal .
Triangular Pyramid How many Faces : Surface Area and Volume.
Triangular pyramid how many faces? A triangular pyramid has 3 faces and one base , we can say it has all together 4 faces as we see a Tetrahedron has 4 faces each one is an equilateral triangle so any face may be considered as the base .
Surface Area
S.A = Area of base + 3 ( Area of a face ) = 1/2 s a + 3 ( 1/2 s l )
S.A = 1/2 x s a + 3/2 s l sq.units. where ' a ' is the height of base triangle , ' s ' is the side length of the base triangle which is again the base of the face triangle , ' l ' is the slant height or the height of the face triangle .
For a tetrahedron surface area S.A = 4 ( 1/2 s a ) = 2 s a , where ' s ' is the base of any face and ' a ' is the height or slant height .
Volume
Volume of a triangular pyramid is given by...
V = 1/3 times Area of base triangle times height of the pyramid .
V = 1/3 x ( 1/2 s a ) h = 1/6 s a h cubic units
Triangular Pyramid How many Faces:example Problems
Ex 1: Find the surface area and volume of the given triangular pyramid .
Sol : Surface area S.A = area of base + area of three faces ( s = 6 cm , a = 4 cm , l = 8 cm , h = 5 cm )
area of base = 1/2 sa = 1/2 x 6 x 4 = 12 cm2, area of three faces = 3/2 (sl) = 3/2 ( 6 x 8 ) = 3 ( 24 ) = 72 cm2
Therefore S.A = 12 cm + 72 cm = 842 cm
Volume V = 1/6 sah = 1/6 x 6 x 4 x 5 = 20 cm3
Ex 2 : The surface area of a tetrahedron is 112 m2 , find the area of the base.
Sol: A tetrahedron has four congruent faces , the area of all four faces are equal and any face can be considered as base.
So , The area of the base in the given tetrahedron = 112/4 = 28 m2 .
Algebra is widely used in day to day activities watch out for my forthcoming posts on polynomials and factoring and factoring polynomials degree 3. I am sure they will be helpful.
