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Surface Area Help.

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Hello! I need to find the surface area of these but I don't understand it very well. I've been stuck on these for a while. Please help! Sorry.

Aug 29, 2018

#1
+100516
+1

First one

We have two triangles comprising the top/bottom  each with a base of 17 cm and a height of 4.9 cm

The area of these  =  17 (4.9)  = 68.6 cm^2

The sides are three rectangles...each with a height of  9cm  and  widths of  [ 7 , 13 and 17 cms]

The total area of these  is  [ 9 ] * [ 7 + 13 + 17  ] =  9 [ 37]  =  333 cm^2

So...the total surface area of the first  figure [ a triangular prism ]  is  [ 68.6 + 333 ] cm^2  =  401.6 cm^2

Aug 29, 2018
#2
+100516
+1

Second one

This is a hexagonal prism

The top and bottom are hexagons...comprised of 6 congruent triangles...each with a base  of 11  ft and a height of 9.5 ft

So...the area of the top/bottom  =  6 (1/2)(11)(9.5)  =  313.5 ft^2

The sides are 6 congruent rectangles   each with a height of  6ft and a width of 11 ft...so the area of the sides is

6 * (11) ( 6)  =396 ft^2

So...the total surface area  =   [313.5 + 396 ] ft^2   =  709.5 ft^2

Aug 29, 2018
#3
+100516
+1

Third one

Another triangular prism

The top/bottom  are  triangles with a base of 15m  and a height  of 11.2 m

So...the area of the top/bottom  is  15 * 11.2  = 168 m^2

The sides are rectangles  each with a height of 7m  and  widths of  [ 13, 14 and 15 ] m

So...the total area of the sides  =  7 [ 13 + 14 + 15  ] = 294 m^2

So...the total surface area  is   168 + 294   =  462 m^2

Aug 29, 2018
#4
+100516
+1

Last one....this is the most difficult

We have a trapezoidal prism

The area of the two trapezoids forming the sides  =

2 * (1/2) (height) ( sum of the base lengths )  =

2 *(1/2) (7.8) ( 17 + 8 )    =  195 m^2

We have two other congruent sides that are rectangles  with height  = 9m  and width  = 8 m

So..their combined area  =  2 * 9 * 8    = 144 m^2

And the top is a rectangle  with dimensions of  8 and 17

So its area is  8 * 17  = 136m^2

And the bottom is a square with a side of  8  ...so its area  = 8^2  = 64 m^2

So...the total surface area  is  195  + 144 + 136 + 64  = 539  m^2

Aug 29, 2018
#5
+1

Thank you so much! I appreciate your help!

Guest Aug 29, 2018