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I'm trying so hard to understand this, but I am currently failing geometry just because of this unit. I tried looking up information, writing notes, everything. Hopefully someone can help me ASAP. Please and thank you for all your help.

 

1. The base of a regular pyramid is a hexagon.

 

What is the area of the base of the pyramid?

Enter your answer in the box. Express your answer in radical form.

 

____ cm2

 

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2. This image shows a square pyramid.

 

What is the surface area of this square pyramid?

25 ft²

100 ft²

125 ft²

200 ft²

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3.

 

What is the surface area of this square pyramid?

 

Round your answer to the nearest tenth, if necessary.

4 yd²

25.1 yd²

36.7 yd²

57.8 yd²

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4.

What is the lateral area of this regular octagonal pyramid?

 

114.8 cm²

162.4 cm²

229.7 cm²

281.3 cm²

Guest Mar 19, 2018
 #1
avatar+89775 
+2

1.  We have 12 congruent triangles here

 

We can find the base of each  as

 

cos 60  =  base/14    

 1/2  = base / 14      multiply both sides by 14

7  = base

 

We can find the height of each as

 

sin 60  =  a / 14     

√3/2  = a / 14    multiply both sides by 14

7√3  = a

 

So......the area of the hexagon is

 

12  * (1/2) (base)(height)  =

 

6 ( 7) (7√3)  =  294√3  cm^2

 

 

cool cool cool

CPhill  Mar 19, 2018
 #2
avatar+89775 
+2

2.  For the lateral surface area, we have 8 congruent triangles  each with the same base as the height because both are opposite 45 degree angles

 

The base of each triangle  =  height  =  5

 

So....the lateral surface area  =

 

8 (1/2) (base) (height)  =

4 (5)(5)  =  100

 

The area of the base  is just  side^2  =  10^2   =  100

 

So.....the  surface area  =  100 + 100  =   200 ft^2

 

 

cool cool cool

CPhill  Mar 19, 2018
 #3
avatar+89775 
+2

3.   We have 8 congruent 30-60-90 triangles

The base of each  =  4.6/ 2   =  2.3

The height of each is opposite the 60° angle  = √3 * base  = √3 * 2.3

 

So.....the lateral surface area  is

 

8 (1/2) (base) (height) =

4 (2.3)(√3 * 2.3)  ≈  36.65 yd^2 

 

The base area  =  side^2  =  4.6^2  = 21.16 yd^2

 

So....the total area  is     36.65 + 21.16  =  57.8 yd^2

 

 

cool cool cool

CPhill  Mar 19, 2018
 #4
avatar+89775 
+2

Last one

 

We have 8 congruent triangles each with a base  of 5.8 cm

 

We can use the Pythagorean Theorem to find the slant height of each  =

 

√[ 7^2 + 7^2]  =  √ [2 * 7^2]   =  7√2

 

So.....the lateral area  is

 

8 (1/2) (base) (slant height)  =

 

4 (5.8) (7√2 )  =  229. 7 cm^2

 

 

cool cool cool

CPhill  Mar 19, 2018

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