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, s=12 inches, s2=12 inches, s3 = 17 and l=10 inches.
To find the surface area, we need to find the area of its five faces, which are composed of 2 triangular bases and 3 rectangular sides.
1. Triangular bases (2 bases):
Since the triangular bases are identical from the numbers given, we can find the area of one triangle and multiply it by 2.
Area of triangle = 0.5 × base × height
Area of triangle = 0.5 × 17 × 9
Area of triangle = 76.5 square inches
To find the total area for the 2 triangular bases, we multiply this value by 2:
2 * 76.5 = 153 square inches
2. Rectangular sides (3 sides):
The dimensions given indicate that these rectangular sides are identical. So, we can find the area of one rectangle and multiply it by 3.
Area of rectangle = length × width
Area of rectangle = 12 × 10 (taking s as the width, and l as the length)
Area of rectangle = 120 square inches
To find the total area for the 3 rectangular sides, we multiply this value by 3:
3 * 120 = 360 square inches
Now, to find the total surface area of the showcase, we add the areas of the triangles and rectangles:
Surface Area = 153 + 360
Surface Area = 513 square inches
The surface area of the display showcase is 513 square inches.
To find the surface area of the triangular prism display showcase, you need to calculate the areas of each of its individual faces and then add them up.
A triangular prism has two triangle faces and three rectangular faces.
1. Let's start by calculating the areas of the triangular faces:
- Area of the first triangle = (base * height) / 2 = (17 * 9) / 2 = 76.5 square inches
- Area of the second triangle = (base * height) / 2 = (17 * 9) / 2 = 76.5 square inches
2. Now, let's calculate the areas of the rectangular faces:
- Area of the first rectangular face = (side2 * length) = 12 * 10 = 120 square inches
- Area of the second rectangular face = (side2 * length) = 12 * 10 = 120 square inches
- Area of the third rectangular face = (side3 * length) = 17 * 10 = 170 square inches
3. Finally, add up the areas of all the faces to get the total surface area of the display showcase:
Total surface area = Area of Triangle 1 + Area of Triangle 2 + Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3
= 76.5 + 76.5 + 120 + 120 + 170
= 559 square inches
Therefore, the surface area of the display showcase is 559 square inches.
To find the surface area of the display showcase, we need to calculate the area of each face and then sum them up.
Face 1: Base of the triangular prism
The base of the triangular prism is a triangle with base length (b) equal to 17 inches and height (h) equal to 9 inches. The formula to find the area of a triangle is:
Area = 0.5 * base * height
Plugging in the values, we get:
Area 1 = 0.5 * 17 * 9 = 76.5 square inches
Face 2: Rectangle side of the triangular prism
One side of the triangular prism is a rectangle with length (l) equal to 10 inches and height (h) equal to 9 inches. The formula to find the area of a rectangle is:
Area = length * height
Plugging in the values, we get:
Area 2 = 10 * 9 = 90 square inches
Face 3: Triangle side of the triangular prism
The other side of the triangular prism is a triangle with base length (s2) equal to 12 inches and height (h) equal to 9 inches. Again, we can use the formula for the area of a triangle:
Area = 0.5 * base * height
Plugging in the values, we get:
Area 3 = 0.5 * 12 * 9 = 54 square inches
Face 4: Triangle side of the triangular prism
The top face of the triangular prism is also a triangle with base length (s3) equal to 17 inches and height (h) equal to 9 inches. We'll use the same formula for the area of a triangle:
Area = 0.5 * base * height
Plugging in the values, we get:
Area 4 = 0.5 * 17 * 9 = 76.5 square inches
Face 5: Rectangle side of the triangular prism
The remaining side of the triangular prism is another rectangle with length (l) equal to 10 inches and height (s) equal to 12 inches. Once again, the formula for the area of a rectangle is:
Area = length * height
Plugging in the values, we get:
Area 5 = 10 * 12 = 120 square inches
Now, we can sum up the areas of all the faces to find the total surface area of the display showcase:
Total Surface Area = Area 1 + Area 2 + Area 3 + Area 4 + Area 5
= 76.5 + 90 + 54 + 76.5 + 120
= 417 square inches
Therefore, the surface area of the display showcase is 417 square inches.