The shape is 6 cm 7 cm 4 cm and 12 cm 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 fabnic will be left over?
(1 point)
• 324 cm²
• 184 cm²
• 84 cm²
• 240 cm²
To find the total surface area of the triangular prism tent, we first need to calculate the area of each face.
The triangular bases of the prism can be calculated using the formula for the area of a triangle: 1/2 * base * height. The base and height of the triangular face are 6 cm and 4 cm, respectively.
Area of the bottom triangle = 1/2 * 6 cm * 4 cm = 12 cm²
Area of the top triangle = 1/2 * 6 cm * 4 cm = 12 cm²
Next, we calculate the areas of the three rectangular faces. Two of the faces are 6 cm by 7 cm, and the third is 4 cm by 7 cm.
Area of the 6 cm x 7 cm rectangle: 6 cm * 7 cm = 42 cm²
Area of the 4 cm x 7 cm rectangle: 4 cm * 7 cm = 28 cm²
Total surface area of the tent = 2(12 cm²) + 42 cm² + 28 cm² = 94 cm².
The total fabric area is 18 cm * 18 cm = 324 cm².
To find the amount of fabric left over, subtract the total surface area of the tent from the total fabric area:
324 cm² - 94 cm² = 230 cm².
Therefore, the correct answer is:
• 230 cm²