Surface Area Nets

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Answer Key & Explanations

Surface Area Nets · Grade 6 · Worksheet 2

1. Emma is designing a net for a rectangular prism gift box. The net is made up of 6 rectangles. The front and back faces each measure 25 cm by 15 cm. The top and bottom faces each measure 25 cm by 10 cm. The left and right faces each measure 15 cm by 10 cm. What is the total surface area of the gift box? Answer: 1550 cm² Solution: Find the area of the front face. 25 cm × 15 cm = 375 cm². Since the back face is identical, the total area for front and back = 2 × 375 = 750 cm².
   Full step-by-step solution

   Step 1: Find the area of the front face. 25 cm × 15 cm = 375 cm². Since the back face is identical, the total area for front and back = 2 × 375 = 750 cm². Step 2: Find the area of the top face. 25 cm × 10 cm = 250 cm². Since the bottom face is identical, the total area for top and bottom = 2 × 250 = 500 cm². Step 3: Find the area of the left face. 15 cm × 10 cm = 150 cm². Since the right face is identical, the total area for left and right = 2 × 150 = 300 cm². Step 4: Add all the areas together: 750 + 500 + 300 = 1550 cm². The total surface area of the gift box is 1550 cm².

2. A rectangular prism has a net consisting of 6 rectangles. The dimensions are: length = 14 cm, width = 9 cm, and height = 7 cm. What is the total surface area of this rectangular prism? Answer: 574 cm² Solution: Identify the three pairs of identical faces in the rectangular prism: - Two faces with dimensions 14 cm by 9 cm - Two faces with dimensions 14 cm by 7 cm - Two faces with dimensions 9 cm by 7 cm - Area of 14 cm by 9 cm face = 14 × 9 = 126 cm² - Area of 14 cm by 7 cm face = 14 × 7 = 98 cm² - Area…
   Full step-by-step solution

   Step 1: Identify the three pairs of identical faces in the rectangular prism: - Two faces with dimensions 14 cm by 9 cm - Two faces with dimensions 14 cm by 7 cm - Two faces with dimensions 9 cm by 7 cm Step 2: Calculate the area of each type of face: - Area of 14 cm by 9 cm face = 14 × 9 = 126 cm² - Area of 14 cm by 7 cm face = 14 × 7 = 98 cm² - Area of 9 cm by 7 cm face = 9 × 7 = 63 cm² Step 3: Since there are two of each type of face, multiply each area by 2: - Two 14×9 faces: 2 × 126 = 252 cm² - Two 14×7 faces: 2 × 98 = 196 cm² - Two 9×7 faces: 2 × 63 = 126 cm² Step 4: Add all the areas together to find the total surface area: 252 + 196 + 126 = 574 cm² The total surface area of the rectangular prism is 574 cm².

3. Aroha is designing a net for a rectangular prism display case. The net has 6 rectangular faces. The front and back faces each measure 105 cm by 75 cm. The top and bottom faces each measure 105 cm by 35 cm. The left and right faces each measure 75 cm by 35 cm. What is the total surface area of the display case in square centimeters? Answer: 28350 Solution: Find the area of the front face: 105 cm * 75 cm = 7875 cm². The back face is identical, so the total area for the front and back pair is 2 * 7875 = 15750 cm². Find the area of the top face: 105 cm * 35 cm = 3675 cm².
   Full step-by-step solution

   Step 1: Find the area of the front face: 105 cm * 75 cm = 7875 cm². The back face is identical, so the total area for the front and back pair is 2 * 7875 = 15750 cm². Step 2: Find the area of the top face: 105 cm * 35 cm = 3675 cm². The bottom face is identical, so the total area for the top and bottom pair is 2 * 3675 = 7350 cm². Step 3: Find the area of the left face: 75 cm * 35 cm = 2625 cm². The right face is identical, so the total area for the left and right pair is 2 * 2625 = 5250 cm². Step 4: Add the three pair totals: 15750 + 7350 + 5250 = 28350 cm². The total surface area of the display case is 28350 cm².

4. Matiu is creating a model of a rectangular prism for his mathematics project. He draws the net of the prism on grid paper. The net consists of 6 rectangular faces: two faces are 14 cm by 11 cm, two faces are 14 cm by 9 cm, and two faces are 11 cm by 9 cm. What is the total surface area of Matiu's rectangular prism in square centimeters? Answer: 758 Solution: Identify the three different pairs of faces. Pair 1: Two faces measuring 14 cm by 11 cm. Area of one face = 14 cm × 11 cm = 154 square cm.
   Full step-by-step solution

   Step 1: Identify the three different pairs of faces. Pair 1: Two faces measuring 14 cm by 11 cm. Area of one face = 14 cm × 11 cm = 154 square cm. Total area for this pair = 2 × 154 = 308 square cm. Pair 2: Two faces measuring 14 cm by 9 cm. Area of one face = 14 cm × 9 cm = 126 square cm. Total area for this pair = 2 × 126 = 252 square cm. Pair 3: Two faces measuring 11 cm by 9 cm. Area of one face = 11 cm × 9 cm = 99 square cm. Total area for this pair = 2 × 99 = 198 square cm. Step 2: Add the areas of all three pairs to find the total surface area. Total surface area = 308 + 252 + 198 = 758 square cm. The answer is 758.