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.

Guest Aug 29, 2018

#1**+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

CPhill
Aug 29, 2018

#2**+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

CPhill
Aug 29, 2018

#3**+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

CPhill
Aug 29, 2018

#4**+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

CPhill
Aug 29, 2018