To find the surface area of a triangular prism, we need to calculate the area of each of the individual faces and then add them all up.
1. The area of the two triangular bases can be calculated using the formula for the area of a triangle: 1/2*base*height. Since the base and height of the triangle are given as s1=10 inches and l=10 inches respectively, the area of one of the triangular bases is:
Area_base = 1/2 * 10 * 10 = 50 square inches
Since there are two triangular bases, the total area of the bases is: 2*Area_base = 2*50 = 100 square inches
2. The three rectangular faces of the prism can be calculated using the formula for the area of a rectangle: length*width. The length and width of each rectangle are given as l=10 inches and h=9 inches respectively. So, the area of one of the rectangular faces is:
Area_side1 = l * h = 10 * 9 = 90 square inches
Area_side2 = 17 * 9 = 153 square inches
Area_side3 = 17 * 10 = 170 square inches
The total area of the three rectangular faces is: Area_side1 + Area_side2 + Area_side3
= 90 + 153 + 170 = 413 square inches
3. The total surface area of the triangular prism is the sum of the areas of the bases and the areas of the three rectangular faces:
Surface Area = 100 + 413 = 513 square inches
Therefore, the surface area of the display showcase is 513 square inches.
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 answer