Christian collects model car and planes he has a display showcase of all of his collectors items solve this real-world problem to find the the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions h=9inches b=17inches, s1=12inches, s3=17 and 1=10
To find the surface area of the triangular prism showcase, we need to calculate the surface area of each face and then add them up.
1. Calculate the area of the triangular bases:
The formula for the area of a triangle is 1/2 * base * height.
For the base of the triangle, we have b = 17 inches and for the height, we have h = 9 inches.
Area of one base = 1/2 * 17 * 9 = 1/2 * 153 = 76.5 square inches
Now, since the showcase has two triangular bases, the total area of the triangular bases is:
Total area of triangular bases = 2 * 76.5 = 153 square inches
2. Calculate the area of the three rectangular faces:
The formula for the area of a rectangle is length * width.
For the rectangular faces adjoining the triangles, we have:
Face 1: length = 17 inches, width = 12 inches
Face 2: length = 17 inches, width = 10 inches
Face 3: length = 12 inches, width = 10 inches
Area of Face 1 = 17 * 12 = 204 square inches
Area of Face 2 = 17 * 10 = 170 square inches
Area of Face 3 = 12 * 10 = 120 square inches
Total area of the three rectangular faces = 204 + 170 + 120 = 494 square inches
3. Add up the areas of the triangular bases and rectangular faces:
Total surface area of the triangular prism showcase = Total area of triangular bases + Total area of three rectangular faces
Total surface area = 153 + 494 = 647 square inches
Therefore, the surface area of Christian's display showcase is 647 square inches.