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, s2 =12 inches, s3 = 17 and l =10 inches.(1 point) S.A.= in.2
To find the surface area of a triangular prism, we need to calculate the area of the two triangular bases and the three rectangular faces.
First, find the area of the triangular bases:
Area of a triangle = 0.5 * base * height
Area of base 1 = 0.5 * 17 * 9 = 76.5 square inches
Area of base 2 = 0.5 * 17 * 10 = 85 square inches
Next, find the area of the three rectangular faces:
Area of rectangular faces = perimeter of base * height
Perimeter of base = s1 + s2 + s3 = 10 + 12 + 17 = 39 inches
Height = l = 10 inches
Area of face 1 = 39 * 10 = 390 square inches
Area of face 2 = 39 * 9 = 351 square inches
Area of face 3 = 39 * 17 = 663 square inches
Now, find the total surface area by adding the areas of the bases and faces:
Total surface area = 76.5 + 85 + 390 + 351 + 663 = 1565.5 square inches
Therefore, the surface area of the display showcase is 1565.5 square inches.
wronG
I apologize for the mistake. Let's correct the calculation.
First, find the area of the triangular bases:
Area of base 1 = 0.5 * 17 * 9 = 76.5 square inches
Area of base 2 = 0.5 * 10 * 9 = 45 square inches
Next, find the area of the three rectangular faces:
Area of face 1 = 17 * 9 = 153 square inches
Area of face 2 = 10 * 9 = 90 square inches
Area of face 3 = 17 * 9 = 153 square inches
Now, find the total surface area by adding the areas of the bases and faces:
Total surface area = 76.5 + 45 + 153 + 90 + 153 = 517.5 square inches
Therefore, the surface area of the display showcase is 517.5 square inches.