Introduction
Triangular pyramid is one type of three dimensional shapes. It has four vertices. Three vertices are in the base and one vertex is on top of the pyramid. Vertices are nothing but the corner points of the pyramid. The shape of the triangular pyramid is shown in below. In the figure A, A', B, B', C, C' are the vertices. Let us see how to calculate the volume and surface area of the triangular pyramid.
Formula Used to Find Volume and Surface Area of Triangular Pyramid:
Surface area of the triangular pyramid (SA) = A + `(p * l) / (2)` square units
A – Base area
p – Perimeter of base
l – Slant height
Volume of triangular pyramid (V) = `1/3` A h cubic units
A – Area of the base
h – Height of the pyramid
I am planning to write more post on how to factor polynomial, solve the system of linear equations. Keep checking my blog.
Vertices of Triangular Pyramid– Example Problems:
1. The triangular pyramid has the vertices A (0, 0), B (18, 0), slant height (l) = 15 units, height (h) = 12 units. Find the volume and surface area of the triangular pyramid.
Solution:
Given:
A (0, 0), B (18, 0)
Slant height (l) = 15
Height (h) = 12
Length between two vertices (a) =` sqrt ((y_2- y_1)^ 2 + (x_2- x_1)^2)`
= `sqrt((0-0)^2+(18-0)^2)`
= `sqrt(324)`
a = 18 units
Base area (A):
Base area of the triangle (A) = a2 x `sqrt (3) / 4` square units
= 182 x 0.433
= 324 x 0.433
Base area of the triangle (A) = 140.292 square units
Perimeter of the base (P):
Perimeter of the base (p) = 3 a units
= 3 x 18
= 54 units
Surface area (SA):
Surface area of the triangular pyramid (SA) = A + `(p * l) / 2` square units
= 140.292 + `(54 X 15) / 2`
= 140.292 + 405
Surface area of the triangular pyramid (SA) = 545.292 square units
Volume (V):
Volume of triangular pyramid (V) = `1/3` A h cubic units
= `1/3` x 140.292 x 12
= `1/3` x 1683.504
Volume of triangular pyramid (V) = 561.168 cubic units
2. The triangular pyramid has the vertices A (0, 0), B (10, 0), slant height (l) = 7.8 units, height (h) = 6 units. Find the volume and surface area of the triangular pyramid.
Solution:
Given:
A (0, 0), B (10, 0)
Slant height (l) = 7.8
Height (h) = 6
Length between two vertices (a) = `sqrt ((y_2- y_1)^2 + (x_2-x1)^2)`
= `sqrt((0-0)^2+(10-0)^2)`
= `sqrt(100)`
a = 10 units
Base area (A):
Base area of the triangle (A) = a2 x `sqrt (3) / 4 ` square units
= 102 x 0.433
= 100 x 0.433
Base area of the triangle (A) = 43.3 square units
Perimeter of the base (P):
Perimeter of the base (p) = 3 a units
= 3 x 10
= 30 units
Surface area (SA):
Surface area of the triangular pyramid (SA) = A + `(p * l) / 2` square units
= 43.3 + `(30 X 7.8) / 2`
= 43.3 + 117
Surface area of the triangular pyramid (SA) = 160.3 square units
Volume (V):
Volume of triangular pyramid (V) = `1/3` A h cubic units
= `1/3` x 43.3 x 6
= `1/3` x 259.8
Volume of triangular pyramid (V) = 86.6 cubic units
My Previous Blog :- http://advancemath.blogspot.in/2012/09/vertical-line-equation.html
Triangular pyramid is one type of three dimensional shapes. It has four vertices. Three vertices are in the base and one vertex is on top of the pyramid. Vertices are nothing but the corner points of the pyramid. The shape of the triangular pyramid is shown in below. In the figure A, A', B, B', C, C' are the vertices. Let us see how to calculate the volume and surface area of the triangular pyramid.
Formula Used to Find Volume and Surface Area of Triangular Pyramid:
A – Base area
p – Perimeter of base
l – Slant height
Volume of triangular pyramid (V) = `1/3` A h cubic units
A – Area of the base
h – Height of the pyramid
I am planning to write more post on how to factor polynomial, solve the system of linear equations. Keep checking my blog.
Vertices of Triangular Pyramid– Example Problems:
1. The triangular pyramid has the vertices A (0, 0), B (18, 0), slant height (l) = 15 units, height (h) = 12 units. Find the volume and surface area of the triangular pyramid.
Solution:
Given:
A (0, 0), B (18, 0)
Slant height (l) = 15
Height (h) = 12
Length between two vertices (a) =` sqrt ((y_2- y_1)^ 2 + (x_2- x_1)^2)`
= `sqrt((0-0)^2+(18-0)^2)`
= `sqrt(324)`
a = 18 units
Base area (A):
Base area of the triangle (A) = a2 x `sqrt (3) / 4` square units
= 182 x 0.433
= 324 x 0.433
Base area of the triangle (A) = 140.292 square units
Perimeter of the base (P):
Perimeter of the base (p) = 3 a units
= 3 x 18
= 54 units
Surface area (SA):
Surface area of the triangular pyramid (SA) = A + `(p * l) / 2` square units
= 140.292 + `(54 X 15) / 2`
= 140.292 + 405
Surface area of the triangular pyramid (SA) = 545.292 square units
Volume (V):
Volume of triangular pyramid (V) = `1/3` A h cubic units
= `1/3` x 140.292 x 12
= `1/3` x 1683.504
Volume of triangular pyramid (V) = 561.168 cubic units
2. The triangular pyramid has the vertices A (0, 0), B (10, 0), slant height (l) = 7.8 units, height (h) = 6 units. Find the volume and surface area of the triangular pyramid.
Solution:
Given:
A (0, 0), B (10, 0)
Slant height (l) = 7.8
Height (h) = 6
Length between two vertices (a) = `sqrt ((y_2- y_1)^2 + (x_2-x1)^2)`
= `sqrt((0-0)^2+(10-0)^2)`
= `sqrt(100)`
a = 10 units
Base area (A):
Base area of the triangle (A) = a2 x `sqrt (3) / 4 ` square units
= 102 x 0.433
= 100 x 0.433
Base area of the triangle (A) = 43.3 square units
Perimeter of the base (P):
Perimeter of the base (p) = 3 a units
= 3 x 10
= 30 units
Surface area (SA):
Surface area of the triangular pyramid (SA) = A + `(p * l) / 2` square units
= 43.3 + `(30 X 7.8) / 2`
= 43.3 + 117
Surface area of the triangular pyramid (SA) = 160.3 square units
Volume (V):
Volume of triangular pyramid (V) = `1/3` A h cubic units
= `1/3` x 43.3 x 6
= `1/3` x 259.8
Volume of triangular pyramid (V) = 86.6 cubic units
My Previous Blog :- http://advancemath.blogspot.in/2012/09/vertical-line-equation.html
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