We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
49
2
avatar+50 

Hi! I'm having trouble with 2 math problems from my homework, the theorems are not in the book and I am having trouble finding relavant information online.

 

(1) Find the lateral area and volume of a pyramid with a rectangular base of dimensions 32 by 66 and with lateral edge 65.

 

(2) Find the lateral area of a regular pentagonal pyramid with base edge 18 and lateral edge 16.

 Jun 3, 2019
 #1
avatar+8095 
+2

(1)

 

Here,  s  is a slant height and  a  is the altitude.

 

We can find  s  with the Pythagorean theorem.

s2 + 162  =  652

s2  =  652 - 162

s2  =  3969

s  =  63

 

Now we can find  a  with the Pythagorean theorem.

a2 + 332  =  s2

a2 + 332  =  632

a2  =  632 - 332

a2  =  2880

a  =  √[ 2880 ]

a  =  24√5

 

*****edit*****

My original answer for lateral area wasn't right because I didn't take into account that the faces aren't all the same.

 

The same way we found  s ,  we can find the length of the other slant height.

 

other slant height  =  √[ 652 - 332 ]  =  56

 

lateral area   =   2 * (1/2) * 32 * 63   +   2 * (1/2) * 66 * 56   =   32 * 63  +  66 * 56   =   5712  square units

 

And we can check this answer with this handy dandy calculator: here

**************


volume  =  (1/3) * area of base * altitude

volume  =  (1/3) * (32 * 66) * a

volume  =  (1/3) * (32 * 66) * 24√5

volume  =  16896√5  cubic units

 

If you have a question about where any of these numbers came from please ask smiley

 Jun 3, 2019
edited by hectictar  Jun 4, 2019
 #2
avatar+8095 
+3

(2)  Here is a sketch of a single face of the regular pentagonal pyramid:

 

 

Remember there are  5  faces total because a pentagon has  5  sides. So....

 

lateral area  =  5 * area of triangular face

lateral area  =  5 * (1/2)(18)( s )

 

We can find  s  with the Pythagorean theorem:

92 + s2  =  162

s2  =  162 - 92

s2  =  175

s  =  √[ 175 ]

s  =  5√7

 

lateral area  =  5 * (1/2)(18)( 5√7 )

lateral area  =  225√7  square units

 Jun 3, 2019

21 Online Users

avatar
avatar