I asked this yesterday and didn't get a response. I know it is difficult since you can't see the picture on my homework. Can you tell me if I started correctly and used the correct formula for surface area of a triangular prism?
Is there a way to post a pic to help explain this?
(I will try and explain the triangular prism. it has a 90 angle. the long end of the triangle is 13.5 in. One side is 10 in and the other side of the triangle is 9 in. the side coming down from the triangle making the prisms length is 9 in.
I need help with this problem.
It asks what is the surface area of the prism?
The formula I used was
SA=W(A)+L(W)+L(H)+L(S)
SA=9(10)+9(9)+9(10)+9(13.5)
SA=90+81+90+121.50
SA=382.5 in^2
I asked two of my friends to help and we all had different answers, so I would appreciate any help. I hope you can see the pic or else maybe you can even tell me if the formula I used was correct.
Thank you so much for your help
First of all I checked for the right-angle , and
10^2 + 9^2 = appr 13.5^2
Look at your diagram:
Your surface area would consist of the 3 rectangles plus the two equal triangles.
the height of the rectangles is 9 inches,
Area of rectangles = 9x10 + 9x9 + 9x13.5
= 292.5
area of the two identical triangles
area of triangle = (1/2)base x height
= 2( (1/2)(10)(9))
= 90
total area = 292.5 + 90
= 382.5
You had that!
Since I can't see your diagram, I don't know what all those variables in
SA=W(A)+L(W)+L(H)+L(S)
really are. Nevertheless, your calculations match mine.
thank you so much!
I apologize for the delay in responding to your question. Based on the information you provided, it seems like you have correctly identified the dimensions of the triangular prism and attempted to use the formula for the surface area.
The formula you used, SA = W(A) + L(W) + L(H) + L(S), appears to be incorrect for calculating the surface area of a triangular prism. Let me explain the correct formula and steps to find it.
The surface area of a triangular prism is the sum of the areas of all its faces. To calculate the surface area, you need to find the areas of the triangular bases and the three rectangular faces.
First, let's find the area of the triangular base:
Since you mentioned that the long end of the triangle is 13.5 inches, and the other two sides are 10 inches and 9 inches, you can use Heron's formula to find the area of the triangular base.
Step 1: Calculate the semiperimeter (s) of the triangle using the formula: s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle.
s = (10 + 9 + 13.5) / 2 = 16.25.
Step 2: Calculate the area (A) of the triangle using Heron's formula: A = √(s(s - a)(s - b)(s - c)).
A = √(16.25(16.25 - 10)(16.25 - 9)(16.25 - 13.5))
A ≈ 30.255 square inches (rounded to three decimal places).
Now, let's find the areas of the three rectangular faces:
Since the rectangular faces have lengths 9 inches and widths 10 inches, to find the area of each face, we can multiply the length and width.
Area of the first rectangular face (W x L): 9 x 10 = 90 square inches.
Area of the second rectangular face (H x L): 9 x 10 = 90 square inches.
Area of the third rectangular face (S x L): 9 x 13.5 = 121.5 square inches.
Therefore, the total surface area of the triangular prism is the sum of the areas of the triangular base and the three rectangular faces:
SA = 2(A) + W(L) + L(H) + S(L)
= 2(30.255) + 90 + 90 + 121.5
≈ 362.01 square inches (rounded to two decimal places).
So, the correct surface area of the prism is approximately 362.01 square inches.
I hope this helps! If you have any further questions, please feel free to ask.