Christian 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,%C2%A0 s2 =12 inches,%C2%A0 s3 = 17 and l =10 inches.(1 point) S.A.=%C2%A0in.2
BOTS ARE DUMB ITS 543
wrong
To find the surface area of a triangular prism, you first need to find the area of each of the five faces and then add them together.
Area of the two triangular bases:
A = (1/2) * base * height
A = (1/2) * 17 * 10
A = 85 in^2 (for each base)
Area of the three rectangular sides:
(2 * sidelength1 * height) + (2 * sidelength2 * height) + (sidelength3 * actual length)
(2 * 10 * 9) + (2 * 12 * 9) + (17 * 10)
= 180 + 216 + 170
= 566 in^2
Total surface area:
2(85) + 566
= 170 + 566
= 736 in^2
Therefore, the surface area of the display showcase is 736 square inches.
I apologize for the error. Let's calculate the surface area correctly this time.
Surface Area of a Triangular Prism = 2 * Area of Base Triangle + Perimeter of Base Triangle * Height of Prism + 3 * Area of Lateral Faces
Let's first calculate the area of the base triangle:
Area of Base Triangle = (1/2) * base * height
Area of Base Triangle = (1/2) * 17 * 10
Area of Base Triangle = 85 in^2
Next, let's calculate the perimeter of the base triangle:
Perimeter of Base Triangle = s1 + s2 + s3
Perimeter of Base Triangle = 10 + 12 + 17
Perimeter of Base Triangle = 39 inches
Now, calculate the lateral surface area:
Lateral Surface Area = Perimeter of Base Triangle * Height of Prism
Lateral Surface Area = 39 * 9
Lateral Surface Area = 351 in^2
Now, calculate the total surface area:
Surface Area = 2 * Area of Base Triangle + Lateral Surface Area
Surface Area = 2 * 85 + 351
Surface Area = 170 + 351
Surface Area = 521 in^2
Therefore, the correct surface area of the display showcase is 521 square inches.
I apologize for the mistake in my previous responses. Let's recalculate the surface area of the display showcase using the correct calculations.
Surface Area of a Triangular Prism = 2 * Area of Base Triangle + Perimeter of Base Triangle * Height of Prism + 3 * Area of Lateral Faces
Area of Base Triangle = (1/2) * base * height
Area of Base Triangle = (1/2) * 17 * 10
Area of Base Triangle = 85 in^2
Perimeter of Base Triangle = s1 + s2 + s3
Perimeter of Base Triangle = 10 + 12 + 17
Perimeter of Base Triangle = 39 inches
Lateral Surface Area = Perimeter of Base Triangle * Height of Prism
Lateral Surface Area = 39 * 9
Lateral Surface Area = 351 in^2
Total Surface Area = 2 * Area of Base Triangle + Lateral Surface Area
Total Surface Area = 2 * 85 + 351
Total Surface Area = 170 + 351
Total Surface Area = 521 in^2
After recalculating, the surface area of the display showcase is 521 square inches, not 543. Thank you for the correction.