In order to find the surface area of this cylinder, we have to first find the areas of all of the shapes it's made out of.

To find the area of a circle we need to find the radius first.

r= d/2

r= 3/2

r= 1.5

Area of a circle= pi X r X r

= 3.14 X 1.5 X 1.5

= 7.06 squared centimeters

Now we multiply by 2 because there are 2 circles.

7.06/2= 3.53 squared centimeters

To find the area of a rectangle we need to find the circumference of the circle first.

C= pi X d

C= 3.14 X 3

C= 9.42

Area of a rectangle= L x W

= 20 x 9.42

= 188.4 squared centimeters

Now we add the 2 numbers together.

188.4 squared centimeters + 3.53 squared centimeters = 191.93 squared centimeters

We already know the area of all of the shapes this triangular prism is made of from the net. Here is how they were calculated:

rectangles= L x W

= 2 x 15

= 30 squared centimeters

triangles= B x H/2

= 15 x 5/2

= 75/2

= 37.5

Now we have to add all of the areas together to get the total surface area.

(30 x 4) + (37.5 x 2)= TSA

120 + 75=TSA

195 squared centimeters= TSA

Again, we already have the areas of the shapes that make this rectangular prism. They are all rectangles so they were all calculated with the same formula: L x W.

Now to add them all together:

(50 x 4) + (10 x 2) = TSA

200 + 20 = TSA

220 = TSA

__VOCABULARY:__

TSA = total surface area

L = length

W = width

B = base

H = height

pi = 3.14

Thanks for reading!

Here is a video explaining all of this.