Question

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

Answer 1

To find the surface area of a triangular prism, you need to calculate the area of the two triangular bases and the three rectangular faces.

First, calculate the area of the triangular bases:
Area of a triangle = 1/2 * base * height

Base of the triangle = 17 inches
Height of the triangle = 9 inches

Area of one triangular base = 1/2 * 17 * 9 = 76.5 square inches
Since there are two triangular bases, the total area of the triangular bases = 2 * 76.5 = 153 square inches

Next, calculate the area of the three rectangular faces:
Area of a rectangle = length * width

For rectangular face 1:
Length = 10 inches
Width = 10 inches

Area of rectangular face 1 = 10 * 10 = 100 square inches

For rectangular face 2:
Length = 12 inches
Width = 9 inches

Area of rectangular face 2 = 12 * 9 = 108 square inches

For rectangular face 3:
Length = 17 inches
Width = 9 inches

Area of rectangular face 3 = 17 * 9 = 153 square inches

Now, find the total surface area of the triangular prism by adding the areas of the triangular bases and the three rectangular faces:
Total surface area = 153 + 100 + 108 + 153 = 514 square inches

Therefore, the surface area of the display showcase (triangular prism) is 514 square inches.