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 240 cm2 240 cm squared 84 cm2 84 cm squared 324 cm2 324 cm squared 184 cm2 and the measurements are 6cm 7cm 4cm 12cm
To find the surface area of the triangular prism tent, we need to first find the area of each of the three triangles that make up the sides of the prism.
For the two lateral faces:
Area = 0.5 x base x height
Area = 0.5 x 6 cm x 7 cm = 21 cm2
Area of both lateral faces = 21 cm2 x 2 = 42 cm2
For the bases:
Area = base x height
Area = 4 cm x 12 cm = 48 cm2
Area of both bases = 48 cm2 x 2 = 96 cm2
Total surface area of the triangular prism = 42 cm2 + 96 cm2 = 138 cm2
So, there will be 18 cm x 18 cm - 138 cm2 = 324 cm2 of fabric left over.
Therefore, the correct answer is 324 cm2.
is this right
Apologies for the mistake in my previous response.
To find the surface area of the triangular prism tent correctly:
For the two lateral faces:
Area = base x height / 2
Area = 6 cm x 7 cm / 2 = 21 cm2
Area of both lateral faces = 21 cm2 x 2 = 42 cm2
For the bases:
Area = base x height
Area = 18 cm x 4 cm = 72 cm2
Area of both bases = 72 cm2 x 2 = 144 cm2
Total surface area of the triangular prism = 42 cm2 (lateral faces) + 144 cm2 (bases) = 186 cm2
So, there will be 18 cm x 18 cm - 186 cm2 = 48 cm2 of fabric left over.
Therefore, the correct answer is 48 cm2. Thank you for pointing it out.