To calculate the surface area of the triangular prism, we first need to find the area of the two triangular bases and the area of the three rectangular sides.
The formula for the surface area of a triangular prism is given by:
Surface Area = 2(Area of triangle) + (Perimeter of triangle) x height
First, we calculate the area of the triangular base:
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 6 cm x 4 cm = 12 cm^2
Now, we calculate the perimeter of the triangle:
Perimeter of triangle = 6 cm + 7 cm + 4 cm = 17 cm
Now, we calculate the surface area of the triangular bases:
Surface Area of triangular bases = 2 x 12 cm^2 + 17 cm x 12 cm = 24 cm^2 + 204 cm^2 = 228 cm^2
Next, we calculate the area of the three rectangular sides:
Area of rectangular side 1 = 6 cm x 12 cm = 72 cm^2
Area of rectangular side 2 = 7 cm x 12 cm = 84 cm^2
Area of rectangular side 3 = 4 cm x 12 cm = 48 cm^2
Now, we sum up the areas of the two triangular bases and the three rectangular sides:
Total surface area = 228 cm^2 + 72 cm^2 + 84 cm^2 + 48 cm^2 = 432 cm^2
Now, we subtract the total surface area of the triangular prism from the total area of the fabric:
Total area of fabric = 18 cm x 18 cm = 324 cm^2
Fabric leftover = Total area of fabric - Total surface area of the triangular prism
Fabric leftover = 324 cm^2 - 432 cm^2 = -108 cm^2
Since the result is negative, it means that there is not enough fabric to cover the triangular prism, and Jordan needs more fabric to complete the tent for his little sister's dolls.
Use the image to answer the question
Jordan purchased a piece of fabric that is 18 cm x 18 cm in order to make his tent for his little sister‘s dolls, using dimensions for the tent shaped as a triangular prism how much fabric would be left over
The measure are 6 cm 7 cm 4 cm 12 cm
1 answer