Question

PLZ HELP WILL MEDAL AND FAN


What is the surface area of the triangular prism shown with height 5 feet? You can use the formula: SA = 2B + PH.

Answer 1

https://racine.brainhoney.com/Resource/26948139,0/Assets/flvs/math1_v10_gs-xml/res0116/08_00_87_01.gif

Answer 2

eight hundred eighty square feet
nine hundred ten square feet
one thousand two hundred square feet
two thousand five hundred fifty square feet

Answer 3

@paki

Answer 4

Do you understand the given formula for the total surface area of the prism?

Answer 5

not that much

Answer 6

Ok. I'll explain the formula to you then you can use the formula.
A prism is a solid that is created by taking a polygon, the base, and sliding the base a certain distance.

Answer 7

In your case you have a triangular prism. The bases are triangles.

Answer 8

Here is one base of your prism.
This base now slides 5 ft toward the back of the drawing.

Answer 9

There is the prism.
The bases can be any polygon. In your case, the bases are triangles.
The side faces of a prism are always parallelograms.

Answer 10

If the prism is a right prism, like your is, then the side faces are not only parallelograms, but they are rectangles.

Answer 11

Now let's look at the surface area formula.
SA = 2B + PH
The total surface are of a prism is the sum of two components, the area of the bases and the area of the lateral faces.

2B means two times B, the area of the base.
Find the area of a base, and multiply by 2 to account for the are of the two bases.

PH means the perimeter of the base times the height. This gives you the lateral area. This is the area of all the rectangular faces combined.

Answer 12

Now we can work on the two components of the area and find the total surface area.

Answer 13

Base area: 2B
Each base is a triangle.
Looking in the figure, each base is a triangle with base 30 ft and height 16 ft.
How do you find the area of a triangle with base 30 ft and height 16 ft?

Answer 14

multiply

Answer 15

and divide by 2

Answer 16

\(\Large A_{triangle} = \dfrac{bh}{2} \)

Answer 17

so i need to do 30x16/2?

Answer 18

Multiply the base by the height and divide by 2. That is the area of each base.
What do you get?

Answer 19

Yes, exactly. Do that.

Answer 20

240 that is what i got

Answer 21

Correct. That is B, the area of each base. The formula has 2B, the area of both bases, so multiply 240 ft^2 by 2 to find 2B.

Answer 22

so would that be 480

Answer 23

@mathstudent55

Answer 24

Correct.
The 2B part is 480 ft^2.
Now we need to work on the lateral surface area, the surface area of the three rectangular sides.

Answer 25

How do I find out PH?

Answer 26

The lateral surface area is PH.
P is the perimeter of the base. H is the height of the prism.
Looking at the figure, we see the base is a triangle with side lengths 30 ft, 16 ft, and 34 ft.
Can you find P, the perimeter of the triangular base?

Answer 27

80

Answer 28

Correct.
Now look in the figure again.
What is the height of the prism?

Answer 29

16

Answer 30

No. Be careful. I know it can be confusing.
We have two different sides called height here.
The height of the base is 16 ft.
We also have the height of the prism. In this case we need the height of the prism, not the height of the base.

Answer 31

so it would be 5?