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 as a triangular prism, how much fabric will be left over?
Triangle prism dimensions:
S1=4 cm
S2=7 cm
S3=7 cm
Height=6 cm
Length= 12 cm
To find the total surface area of the triangular prism, we need to find the surface area of each face and add them together.
Surface Area of a Triangle:
Area = (1/2) * base * height
Surface Area of a Rectangle:
Area = length * width
Now we can calculate the surface area of each face of the triangular prism:
1. Triangle 1:
Area = (1/2) * 4 cm * 6 cm = 12 cm^2
2. Triangle 2:
Area = (1/2) * 7 cm * 6 cm = 21 cm^2
3. Triangle 3:
Area = (1/2) * 7 cm * 6 cm = 21 cm^2
4. Rectangle 1:
Area = 7 cm * 12 cm = 84 cm^2
5. Rectangle 2:
Area = 4 cm * 12 cm = 48 cm^2
Total Surface Area = 12 cm^2 + 21 cm^2 + 21 cm^2 + 84 cm^2 + 48 cm^2 = 186 cm^2
Now, the total surface area of the triangular prism is 186 cm^2.
Since the fabric purchased by Jordan is 18 cm by 18 cm, the total area of this piece of fabric is 18 cm * 18 cm = 324 cm^2.
Therefore, the fabric left over after making the triangular prism tent is 324 cm^2 - 186 cm^2 = 138 cm^2.
So, Jordan will have 138 cm^2 of fabric left over.
No. The surface area of a trianglur prism is BH+(s1+s2+s3)L
S1 is also the base
Apologies for the mistake in the previous calculation. Let's correct it using the formula you provided.
Given dimensions:
Base of triangle (S1) = 7 cm
Height of triangle (H) = 6 cm
Side 2 of triangle (S2) = 7 cm
Side 3 of triangle (S3) = 4 cm
Length of prism (L) = 12 cm
Surface area of a triangular prism:
Surface area = BH + (S1 + S2 + S3) * L
1. Surface area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 7 cm * 6 cm
Area = 21 cm^2
2. Surface area of the rectangle (Base):
Area = 7 cm * 12 cm
Area = 84 cm^2
3. Surface area of the triangular prism:
Surface area = 21 cm^2 + (7 cm + 7 cm + 4 cm) * 12 cm
Surface area = 21 cm^2 + 18 cm * 12 cm
Surface area = 21 cm^2 + 216 cm^2
Surface area = 237 cm^2
The total surface area of the triangular prism is 237 cm^2.
Since the fabric purchased by Jordan is 18 cm by 18 cm, the total area of this piece of fabric is 18 cm * 18 cm = 324 cm^2.
Therefore, the fabric left over after making the triangular prism tent is 324 cm^2 - 237 cm^2 = 87 cm^2.
So, Jordan will have 87 cm^2 of fabric left over.
No. The base has the same amount of CM as S1
Apologies for the oversight. Let's correct the calculation using the correct formula for the surface area of a triangular prism.
Given dimensions:
Base of triangle (S1) = 7 cm
Height of triangle (H) = 6 cm
Side 2 of triangle (S2) = 7 cm
Side 3 of triangle (S3) = 4 cm
Length of prism (L) = 12 cm
Surface area of a triangular prism:
Surface area = BH + (S1 + S2 + S3) * L
1. Surface area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 7 cm * 6 cm
Area = 21 cm^2
2. Surface area of the rectangle (Base):
Area = 7 cm * 12 cm
Area = 84 cm^2
3. Surface area of the triangular prism:
Surface area = 21 cm^2 + (7 cm + 7 cm + 4 cm) * 12 cm
Surface area = 21 cm^2 + 18 cm * 12 cm
Surface area = 21 cm^2 + 216 cm^2
Surface area = 237 cm^2
The total surface area of the triangular prism is 237 cm^2.
Since the fabric purchased by Jordan is 18 cm by 18 cm, the total area of this piece of fabric is 18 cm * 18 cm = 324 cm^2.
Therefore, the fabric left over after making the triangular prism tent is 324 cm^2 - 237 cm^2 = 87 cm^2.
So, Jordan will have 87 cm^2 of fabric left over.
The base is 7 cm
Apologies for the confusion. Let's correct the calculation based on the corrected base dimension.
Given dimensions:
Base of triangle (S1) = 7 cm
Height of triangle (H) = 6 cm
Side 2 of triangle (S2) = 7 cm
Side 3 of triangle (S3) = 4 cm
Length of prism (L) = 12 cm
Surface area of a triangular prism:
Surface area = BH + (S1 + S2 + S3) * L
1. Surface area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 7 cm * 6 cm
Area = 21 cm^2
2. Surface area of the rectangle (Base):
Area = 7 cm * 12 cm
Area = 84 cm^2
3. Surface area of the triangular prism:
Surface area = 21 cm^2 + (7 cm + 7 cm + 4 cm) * 12 cm
Surface area = 21 cm^2 + 18 cm * 12 cm
Surface area = 21 cm^2 + 216 cm^2
Surface area = 237 cm^2
The total surface area of the triangular prism is 237 cm^2.
Since the fabric purchased by Jordan is 18 cm by 18 cm, the total area of this piece of fabric is 18 cm * 18 cm = 324 cm^2.
Therefore, the fabric left over after making the triangular prism tent is 324 cm^2 - 237 cm^2 = 87 cm^2.
So, Jordan will have 87 cm^2 of fabric left over. Thank you for your patience.
Wait I mean the base is 4 cm
No problem. Let's correct the calculation based on the corrected base dimension of 4 cm.
Given dimensions:
Base of triangle (S1) = 4 cm
Height of triangle (H) = 6 cm
Side 2 of triangle (S2) = 7 cm
Side 3 of triangle (S3) = 7 cm
Length of prism (L) = 12 cm
Surface area of a triangular prism:
Surface area = BH + (S1 + S2 + S3) * L
1. Surface area of the triangle:
Area = 0.5 * base * height
Area = 0.5 * 4 cm * 6 cm
Area = 12 cm^2
2. Surface area of the rectangle (Base):
Area = 4 cm * 12 cm
Area = 48 cm^2
3. Surface area of the triangular prism:
Surface area = 12 cm^2 + (4 cm + 7 cm + 7 cm) * 12 cm
Surface area = 12 cm^2 + 18 cm * 12 cm
Surface area = 12 cm^2 + 216 cm^2
Surface area = 228 cm^2
The total surface area of the triangular prism is 228 cm^2.
Since the fabric purchased by Jordan is 18 cm by 18 cm, the total area of this piece of fabric is 18 cm * 18 cm = 324 cm^2.
Therefore, the fabric left over after making the triangular prism tent is 324 cm^2 - 228 cm^2 = 96 cm^2.
So, Jordan will have 96 cm^2 of fabric left over. Thank you for providing the correct base dimension.
Nooo use the formula BH+(s1+s2+s3)L and that formula only. In short term words, solve 4x6+(4+7+7)12
And then subtract 324 from the equation