To find the surface area of a triangular prism, you need to calculate the area of each of the five faces and then sum them up.
The formula for the surface area of a triangular prism is:
Surface Area = 2 * Base Area + Lateral Area
The base area of a triangular prism is the area of the two triangles at the ends, and the lateral area is the area of the three rectangular faces.
1. Calculate the base area:
The base of the prism is a triangle with base b = 17 inches and height h = 9 inches. The formula for the area of a triangle is:
Area = 0.5 * base * height
Base Area = 0.5 * 17 * 9 = 76.5 square inches
2. Calculate the lateral area:
The lateral area of the prism is the sum of the areas of the three rectangular faces.
Area of each rectangle = side1 * height
Lateral Area = s1 * h + s2 * h + s3 * h
Lateral Area = 10 * 9 + 12 * 9 + 17 * 9
Lateral Area = 90 + 108 + 153 = 351 square inches
3. Calculate the surface area:
Surface Area = 2 * Base Area + Lateral Area
Surface Area = 2 * 76.5 + 351
Surface Area = 153 + 351
Surface Area = 504 square inches
Therefore, the surface area of the display showcase is 504 square inches.
QuestionChristian collects model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h =9 inches, b =17 inches, s1 =10 inches, s2 =12 inches, s3 = 17 and l =10 inche
3 answers
wrong
I apologize for the mistake. Let's recalculate the surface area of the triangular prism display showcase with the given dimensions.
Given dimensions:
h = 9 inches (height)
b = 17 inches (base)
s1 = 10 inches (side 1)
s2 = 12 inches (side 2)
s3 = 17 inches (side 3)
l = 10 inches (length)
To find the surface area of a triangular prism, we need to calculate the area of each of the five faces and then sum them up.
1. Calculate the base area:
The base of the prism is a triangle with base b = 17 inches and height h = 9 inches. The formula for the area of a triangle is:
Area = 0.5 * base * height
Base Area = 0.5 * 17 * 9 = 76.5 square inches
2. Calculate the lateral area:
The lateral area of the prism is the sum of the areas of the three rectangular faces.
First, calculate the perimeter of the triangular base:
Perimeter = s1 + s2 + s3 = 10 + 12 + 17 = 39 inches
Next, calculate the lateral area of the prism:
Lateral Area = Perimeter * l = 39 * 10 = 390 square inches
3. Calculate the surface area:
Surface Area = 2 * Base Area + Lateral Area
Surface Area = 2 * 76.5 + 390
Surface Area = 153 + 390
Surface Area = 543 square inches
Therefore, the correct surface area of the display showcase is 543 square inches. Thank you for pointing out the error.
Given dimensions:
h = 9 inches (height)
b = 17 inches (base)
s1 = 10 inches (side 1)
s2 = 12 inches (side 2)
s3 = 17 inches (side 3)
l = 10 inches (length)
To find the surface area of a triangular prism, we need to calculate the area of each of the five faces and then sum them up.
1. Calculate the base area:
The base of the prism is a triangle with base b = 17 inches and height h = 9 inches. The formula for the area of a triangle is:
Area = 0.5 * base * height
Base Area = 0.5 * 17 * 9 = 76.5 square inches
2. Calculate the lateral area:
The lateral area of the prism is the sum of the areas of the three rectangular faces.
First, calculate the perimeter of the triangular base:
Perimeter = s1 + s2 + s3 = 10 + 12 + 17 = 39 inches
Next, calculate the lateral area of the prism:
Lateral Area = Perimeter * l = 39 * 10 = 390 square inches
3. Calculate the surface area:
Surface Area = 2 * Base Area + Lateral Area
Surface Area = 2 * 76.5 + 390
Surface Area = 153 + 390
Surface Area = 543 square inches
Therefore, the correct surface area of the display showcase is 543 square inches. Thank you for pointing out the error.