Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped like a triangular prism, how much fabric will be left over?

Question

Georgia Milestones Grade 7 Mathematics Formula Sh

Answer 1

The formula for finding the surface area of a triangular prism is:

Surface Area = 2 * base area + lateral area

The base area of the triangular prism is the area of the two triangles on the ends of the prism. Since the fabric purchased by Jordan is 18 cm by 18 cm, the base area of each triangle is:

Base area = 1/2 * base * height
Base area = 1/2 * 18 cm * 18 cm
Base area = 162 cm^2

Since there are two triangles, the total base area is:

Total base area = 2 * 162 cm^2
Total base area = 324 cm^2

The lateral area of the triangular prism is the area of the three rectangular sides of the prism. Since the fabric purchased is 18 cm wide, the height of the prism is also 18 cm. The lateral area is:

Lateral area = perimeter of base * height
Lateral area = 3 * 18 cm * 18 cm
Lateral area = 972 cm^2

So, the total surface area of the triangular prism is:

Surface Area = 2 * 324 cm^2 + 972 cm^2
Surface Area = 648 cm^2 + 972 cm^2
Surface Area = 1620 cm^2

Since the fabric purchased by Jordan is 18 cm by 18 cm, the total area of the fabric is:

Total fabric area = 18 cm * 18 cm
Total fabric area = 324 cm^2

Therefore, the amount of fabric left over after making the tent shaped like a triangular prism is:

Leftover fabric = Total fabric area - Surface Area
Leftover fabric = 324 cm^2 - 1620 cm^2
Leftover fabric = -1296 cm^2

Since the leftover fabric is negative, it means that Jordan will need more fabric to make the tent shaped like a triangular prism.