Applications of Surface Area of Prisms Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. 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? (1 point) Responses 324 cm2 324 cm squared 240 cm2 240 cm squared 84 cm2 84 cm squared 184 cm2
The surface area of a triangular prism is calculated by finding the area of the two triangular faces and the three rectangular faces before adding them all together.
The two triangular faces would have an area of 1/2 * base * height = 1/2 * 18 cm * 18 cm = 162 cm^2 each
The three rectangular faces would have an area of length * width = 18 cm * 18 cm = 324 cm^2 each
So the total surface area of the fabric used for the tent would be 2(162 cm^2) + 3(324 cm^2) = 648 cm^2.
Since Jordan purchased a 18 cm by 18 cm piece of fabric, the total area available is also 324 cm^2.
Therefore, the fabric left over would be 324 cm^2 - 648 cm^2 = - 324 cm^2.
There would be 324 cm^2 of fabric left over; none would be left.
The correct response is 324 cm^2.
b=4
h=7
l=12
6
To calculate the surface area of the prism with the given dimensions, we need to use the formula for the surface area of a rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Given:
b = 4 (base)
h = 7 (height)
l = 12 (length)
Substitute the given values into the formula:
Surface Area = 2(12)(7) + 2(12)(4) + 2(4)(7)
Surface Area = 2(84) + 2(48) + 2(28)
Surface Area = 168 + 96 + 56
Surface Area = 320
Therefore, the surface area of the prism with dimensions b=4, h=7, and l=12 is 320 square units.
it's a triangular prism
Apologies for the confusion. If it is a triangular prism, then the calculations will be different. We will use the formula for the surface area of a triangular prism:
Surface Area = 2*(base area) + (perimeter of base)*(height)
Given:
Base of the triangle (b) = 4
Height of the triangle (h) = 7
Length (l) = 12
First, determine the area of the triangular base using the formula for the area of a triangle:
Base Area = (1/2) * base * height
Base Area = (1/2) * 4 * 7
Base Area = 14 square units
Next, calculate the perimeter of the base of the triangle:
Perimeter of base = 3 * base (since it's an equilateral triangle)
Perimeter of base = 3 * 4
Perimeter of base = 12 units
Now, substitute these values into the surface area formula for a triangular prism:
Surface Area = 2 * (14) + 12 * 7
Surface Area = 28 + 84
Surface Area = 112 square units
Therefore, the surface area of the triangular prism with base dimensions b=4, h=7, and length l=12 is 112 square units.
Applications of Surface Area of Prisms Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. 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? (1 point) Responses 324 cm2 324 cm squared 240 cm2 240 cm squared 84 cm2 84 cm squared 184 cm2
it's a triangular prism
b=4
h=7
l=12
one of the side length is 6
Given the dimensions of the triangular prism:
Base dimension (b) = 4
Height (h) = 7
Length (l) = 12
One of the side lengths = 6
To calculate the surface area of the triangular prism, we must first find the area of the triangular base and the perimeter of the base.
Firstly, calculate the area of the triangular base using the Triangle Area formula:
Base Area = 1/2 * base * height
Base Area = 1/2 * 4 * 7
Base Area = 14 square units
Next, determine the perimeter of the base of the triangle since the triangular prism is equilateral:
Perimeter of base = number of sides * side length
Perimeter of base = 3 * 6
Perimeter of base = 18 units
Now, we can use these values to find the total surface area of the triangular prism:
Surface Area = 2 * Base Area + Perimeter of base * height
Surface Area = 2 * 14 + 18 * 12
Surface Area = 28 + 216
Surface Area = 244 square units
Given that the piece of fabric purchased by Jordan is 18 cm by 18 cm, the total area available is 324 square cm.
To find the fabric left over, subtract the surface area of the triangular prism from the total fabric purchased:
Fabric left over = Total fabric purchased - Surface Area of prism
Fabric left over = 324 - 244
Fabric left over = 80 square units
Therefore, there will be 80 square cm of fabric left over. The correct response is 80 cm squared.