Christian collects model cars and planes he has a display show case 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 triangle prism will the following dimensions h= 9 inches b=17 inches s1=10inches s2=12 inches s3=17 and l =10 inches

Answer 1

To find the surface area of the triangular prism showcase, we first need to find the area of each of the three faces, and then add them up.

1. The base (triangle) of the prism has a base of 17 inches (b) and a height of 9 inches (h). The area of a triangle is given by the formula A = 0.5 * base * height. Plugging in the values, we get:
A(base) = 0.5 * 17 * 9 = 76.5 square inches

2. The two side faces are trapezoids. The formula for the area of a trapezoid is A = 0.5 * (s1 + s2) * height.
For the first side face:
A(side1) = 0.5 * (10 + 12) * 10 = 110 square inches

For the second side face:
A(side2) = 0.5 * (12 + 17) * 10 = 145 square inches

3. Now, we add up the areas of all three faces to get the total surface area of the showcase:
Total surface area = A(base) + A(side1) + A(side2)
Total surface area = 76.5 + 110 + 145
Total surface area = 331.5 square inches

Therefore, the surface area of the display showcase is 331.5 square inches.