a.
To find: The pyramid is regular with rectangular dimensions as 40 and 30.
a.
Answer to Problem 3PSA
The pyramid is not regular because all the lateral faces are not equal.
Explanation of Solution
Given information:
A pyramid has rectangular base with dimensions as 40 and 30.
Formula used:
The below theorem is used:
Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
In right
Area of triangle:
b = base of triangle
h = height of triangle
Calculation:
Draw altitude perpendicular to base.
The altitude AD can be calculated by applying Pythagoras Theorem.
In right angle triangle ABC , we get
The altitude AD drawn perpendicular divides the triangle face into two right
Lateral face is triangle.
Area of lateral face 1
Area of lateral face 1
In right angle triangle AFE , we get
The altitude AF drawn perpendicular divides the triangle face into two right triangles of
Lateral face is triangle.
Area of lateral face 2
Area of lateral face 2
Area of lateral face 1
The pyramid is not regular because all the lateral faces are not equal.
b.
To calculate: The lateral area of pyramid with rectangular dimensions as 40 and 30.
b.
Answer to Problem 3PSA
The lateral area of pyramid is
Explanation of Solution
Given information:
A pyramid has rectangular base with dimensions as 40 and 30.
Formula used:
The below theorem is used:
Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
In right angle triangle,
Area of triangle:
b = base of triangle
h = height of triangle
Calculation:
Draw altitude perpendicular to base.
The altitude AD can be calculated by applying Pythagoras Theorem.
In right angle triangle ABC , we get
The altitude AD drawn perpendicular divides the triangle face into two right triangles of
Lateral face is triangle.
Area of lateral face 1
Area of lateral face 1
In right angle triangle AFE , we get
The altitude AF drawn perpendicular divides the triangle face into two right triangles of
Lateral face is triangle.
Area of lateral face 2
Area of lateral face 2
Lateral area of pyramid = (2
Lateral area of pyramid
Lateral area of pyramid
c.
To find: The total area of pyramid with rectangular dimensions as 40 and 30.
c.
Answer to Problem 3PSA
The total area of pyramid is
Explanation of Solution
Given information:
A pyramid has rectangular base with dimensions as 40 and 30.
Formula used:
The below theorem is used:
Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
In right angle triangle,
Area of triangle:
b = base of triangle
h = height of triangle
Area of rectangle:
l = length of rectangle
w= width of rectangle Total Area = Lateral Area + Area of Rectangular Base
Calculation:
Draw altitude perpendicular to base.
The altitude can be calculated by applying Pythagoras Theorem.
In right angle triangle ABC , we get
The altitude AD drawn perpendicular divides the triangle face into two right triangles of
Lateral face is triangle.
Area of lateral face 1
Area of lateral face 1
In right angle triangle AFE , we get
The altitude AF drawn perpendicular divides the triangle face into two right triangles of
Lateral face is triangle.
Area of lateral face 2
Area of lateral face 2
Lateral area of pyramid = ( 2
Lateral area of pyramid
Lateral area of pyramid
Area of rectangular base
Area of rectangular base
Total Area = Lateral Area + Area of Rectangular Base
Total Area
Total Area
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning