Surface Area Nets

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Surface Area Nets · Grade 6 · Worksheet 2

1. Noah is building a wooden storage chest for his camping gear. The chest is shaped like a rectangular prism with length 1.5 meters, width 0.8 meters, and height 0.6 meters. He needs to calculate the total surface area to determine how much wood to buy for all the exterior surfaces. What is the total surface area of the storage chest in square meters? Answer: 5.16 Solution: Identify the dimensions: length = 1.5 m, width = 0.8 m, height = 0.6 m Calculate the area of the front and back faces: 2 × (length × height) = 2 × (1.5 × 0.6) = 2 × 0.9 = 1.8 square meters Calculate the area of the two side faces: 2 × (width × height) = 2 × (0.8 × 0.6) = 2 × 0.48 = 0.96 square…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 1.5 m, width = 0.8 m, height = 0.6 m Step 2: Calculate the area of the front and back faces: 2 × (length × height) = 2 × (1.5 × 0.6) = 2 × 0.9 = 1.8 square meters Step 3: Calculate the area of the two side faces: 2 × (width × height) = 2 × (0.8 × 0.6) = 2 × 0.48 = 0.96 square meters Step 4: Calculate the area of the top and bottom faces: 2 × (length × width) = 2 × (1.5 × 0.8) = 2 × 1.2 = 2.4 square meters Step 5: Add all the areas together: 1.8 + 0.96 + 2.4 = 5.16 square meters The total surface area is 5.16 square meters.

2. Noah is designing a custom gift box for his friend's birthday. The box is shaped like a rectangular prism with dimensions 15 cm in length, 10 cm in width, and 8 cm in height. He wants to cover the entire outside of the box with decorative paper. What is the total surface area of the box that Noah needs to cover in square centimeters? Answer: 700 Solution: Identify the dimensions: length = 15 cm, width = 10 cm, height = 8 cm Calculate the area of the front and back faces: 2 × (length × height) = 2 × (15 × 8) = 2 × 120 = 240 cm² Calculate the area of the left and right faces: 2 × (width × height) = 2 × (10 × 8) = 2 × 80 = 160 cm² Calculate the area…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 15 cm, width = 10 cm, height = 8 cm Step 2: Calculate the area of the front and back faces: 2 × (length × height) = 2 × (15 × 8) = 2 × 120 = 240 cm² Step 3: Calculate the area of the left and right faces: 2 × (width × height) = 2 × (10 × 8) = 2 × 80 = 160 cm² Step 4: Calculate the area of the top and bottom faces: 2 × (length × width) = 2 × (15 × 10) = 2 × 150 = 300 cm² Step 5: Add all the areas together: 240 + 160 + 300 = 700 cm² The total surface area is 700 square centimeters.

3. A square pyramid has a net consisting of one square base with side length 12 cm and four congruent isosceles triangles. Each triangular face has a base of 12 cm and a slant height of 10 cm. What is the total surface area of this square pyramid? Answer: 384 cm² Solution: Calculate the area of the square base. Area = side × side = 12 cm × 12 cm = 144 cm². Calculate the area of one triangular face.
   Full step-by-step solution

   Step 1: Calculate the area of the square base. Area = side × side = 12 cm × 12 cm = 144 cm². Step 2: Calculate the area of one triangular face. Area of triangle = (1/2) × base × height = (1/2) × 12 cm × 10 cm = 60 cm². Step 3: Calculate the total area of all four triangular faces. Total triangular area = 4 × 60 cm² = 240 cm². Step 4: Calculate the total surface area by adding the base area and the triangular area. Total surface area = 144 cm² + 240 cm² = 384 cm². The answer is 384 cm².

4. A net of a rectangular prism has faces with areas: 21 cm², 21 cm², 35 cm², 35 cm², 15 cm², 15 cm². What is the total surface area? Answer: 142 Solution: Identify all six faces of the rectangular prism from the net: two faces of 21 cm², two faces of 35 cm², and two faces of 15 cm². Add the areas of the two 21 cm² faces: 21 + 21 = 42 cm².
   Full step-by-step solution

   Step 1: Identify all six faces of the rectangular prism from the net: two faces of 21 cm², two faces of 35 cm², and two faces of 15 cm². Step 2: Add the areas of the two 21 cm² faces: 21 + 21 = 42 cm². Step 3: Add the areas of the two 35 cm² faces: 35 + 35 = 70 cm². Step 4: Add the areas of the two 15 cm² faces: 15 + 15 = 30 cm². Step 5: Add all the totals together: 42 + 70 + 30 = 142 cm². The answer is 142.

5. A net of a rectangular prism is shown. The net has faces with dimensions: 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 surface area of the rectangular prism? Answer: 758 Solution: Identify the three pairs of identical faces. Pair 1: two faces are 14 cm by 11 cm. Area of one face = 14 × 11 = 154 square cm.
   Full step-by-step solution

   Step 1: Identify the three pairs of identical faces. Pair 1: two faces are 14 cm by 11 cm. Area of one face = 14 × 11 = 154 square cm. Two faces = 2 × 154 = 308 square cm. Step 2: Pair 2: two faces are 14 cm by 9 cm. Area of one face = 14 × 9 = 126 square cm. Two faces = 2 × 126 = 252 square cm. Step 3: Pair 3: two faces are 11 cm by 9 cm. Area of one face = 11 × 9 = 99 square cm. Two faces = 2 × 99 = 198 square cm. Step 4: Add all the areas: 308 + 252 + 198 = 758 square cm. The answer is 758.