triangular prism
the slanted sides on the whole shape is 7 cm
the height is 6 cm
the width is 4 cm
the length is 12 cm
Determine the area of the triangular base of the prism.
square centimeters
Determine the area of the smallest rectangle of the prism.
square centimeters
Determine the area of the largest rectangle of the prism.
square centimeters
What is the total surface area of the triangular prism?
square centimeters
Skip to navigation
To find the area of the triangular base of the prism, we can use the formula for the area of a triangle: 1/2 * base * height. In this case, the base is 4 cm and the height is 6 cm.
Area of the triangular base = 1/2 * 4 cm * 6 cm = 12 square cm
To find the area of the smallest rectangle, we can use the formula for the area of a rectangle: length * width. In this case, the length is 12 cm and the width is 4 cm.
Area of the smallest rectangle = 12 cm * 4 cm = 48 square cm
To find the area of the largest rectangle, we use the same formula: length * width. The length is 12 cm and the width is 7 cm (slanted side of the prism).
Area of the largest rectangle = 12 cm * 7 cm = 84 square cm
To find the total surface area of the triangular prism, we need to sum the areas of the triangular base, two triangular sides, and two rectangular sides.
Total surface area = 2 * Area of triangular base + 2 * Area of smallest rectangle + Area of largest rectangle
Total surface area = 2 * 12 square cm + 2 * 48 square cm + 84 square cm = 24 + 96 + 84 = 204 square cm
Therefore, the total surface area of the triangular prism is 204 square cm.
make sure you use the (7th Grade Math Formula Chart
To find the area of the triangular base of the prism, we can use the formula for the area of a triangle: 1/2 * base * height. In this case, the base is 4 cm and the height is 6 cm.
Area of the triangular base = 1/2 * 4 cm * 6 cm = 12 square cm
Now, let's use the 7th grade math formula chart:
The area of a triangle:
A = 1/2 * base * height
The area of a rectangle:
A = length * width
The total surface area of the prism is calculated as follows:
Area of both triangular sides = 2 * 1/2 * base * height = 2 * 1/2 * 4 cm * 6 cm = 2 * 2 * 6 = 24 square cm
Area of smallest rectangle = length * width = 12 cm * 4 cm = 48 square cm
Area of largest rectangle = length * width = 12 cm * 7 cm = 84 square cm
Total surface area = 2 * Area of triangular base + 2 * Area of rectangular sides + Area of largest rectangle
Total surface area = 2 * 12 square cm + 2 * 48 square cm + 84 square cm
Total surface area = 24 square cm + 96 square cm + 84 square cm
Total surface area = 204 square cm
Therefore, the total surface area of the triangular prism is 204 square cm.
what's the answers
Apologies for missing that earlier. Here are the answers to the questions:
1. Area of the triangular base of the prism: 12 square centimeters
2. Area of the smallest rectangle of the prism: 48 square centimeters
3. Area of the largest rectangle of the prism: 84 square centimeters
4. Total surface area of the triangular prism: 204 square centimeters
I hope this clarifies things. Let me know if you need any more help.