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Bob used his unit cube blocks to make a pyramid (see below). What is the total surface area of this shape?

 

 May 14, 2020
 #1
avatar+980 
0

So we know That the base is 4*4 = 16 units large.

 

The sides give us 4*4 = 16 units.

 

The top is the 16 minus the above layer's base(3*3= 9) so 16-9 = 7.

 

The 3*3 layer has 3*4 =12 on the sides, and 9-4 = 5 for the top.

 

The 2*2 layer has 4*2 = 8 on the sides, and 4-1 = 3 for the top. 

1*1 has 1*4 for the sides, and 1 for the top.

 

Adding together: 16+16 + 7 + 12 + 5 + 8 + 3 + 4 + 1 = 72

 

If you don't understand anything feel free to ask!

 May 14, 2020
 #2
avatar+111456 
+3

Thanks, hugo!!!

 

A fast way to calculate this

 

Area of base  + area of sides  + area  of  top layers  =

 

4^2  +  4 ( 4  +  3 + 2 +1)  + [ (4^2 - 3^2) + (3^2 - 2^2) + (2^2 - 1^2) + (1^2 - 0^2)]  

 

16 + 4(10) + ( 7 + 5 + 3 + 1) =

 

16 + 40 + 16 =

 

72

 

Just as hugo found!!!!!

 

 

cool cool cool

 May 14, 2020

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