Christian collects model, cars and planes. He has a display case of all his collector items solve the real world problems to find the surface area of the display showcase. If it is the shape of a triangle prism with the following dimensions height equals 9 inches base equals 17 inches is one equals 10 inches two equals 12 inches is three equals 17 inches and length equals 10 inches.
To find the surface area of the triangular prism display case, we need to calculate the area of each of the individual surfaces and then sum them up.
First, calculate the area of the triangular base:
Area of a triangle = 1/2 * base * height
Area of the triangle = 1/2 * 17 inches * 9 inches = 76.5 square inches
Next, calculate the area of the two triangular sides:
Area of a triangle = 1/2 * base * height
Area of the triangle one = 1/2 * 10 inches * 12 inches = 60 square inches
Area of the triangle two = 1/2 * 12 inches * 17 inches = 102 square inches
Finally, calculate the area of the three rectangular sides:
Area of a rectangle = length * height
Area of side one = 10 inches * 9 inches = 90 square inches
Area of side two = 10 inches * 12 inches = 120 square inches
Area of side three = 10 inches * 17 inches = 170 square inches
Now, sum up all the individual surface areas:
Total surface area = 76.5 + 60 + 102 + 90 + 120 + 170 = 618.5 square inches
Therefore, the surface area of Christian's triangular prism display case is 618.5 square inches.