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Area and Surface Formulas

Grade 7 · Geometry · Worksheet 1

  1. Ava is building a decorative garden shed with a unique roof. The roof is a square pyramid. The square base of the pyramid has a side length of 6 meters, and each triangular face has a slant height of 11 meters. Ava needs to cover the entire roof (all four triangular faces and the square base) with weatherproof shingles. What is the total surface area of the roof in square meters?
    Answer: ______________
  2. Aroha is painting a cylindrical storage tank. The tank has a radius of 9 cm and a height of 15 cm. What is the total surface area of the tank? (Use π = 3.14)
    Answer: ______________
  3. A cylinder has a radius of 14 cm and a height of 25 cm. Calculate its total surface area. (Use π = 22/7)
    Answer: ______________
  4. Liam is designing a rectangular prism-shaped fish tank for his science project. The tank will be 2.5 meters long, 1.8 meters wide, and 1.2 meters high. He needs to calculate the total surface area to determine how much glass he needs to buy. What is the total surface area of the fish tank in square meters? Answer: ______________
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Answer Key & Explanations

Area and Surface Formulas · Grade 7 · Worksheet 1

  1. Ava is building a decorative garden shed with a unique roof. The roof is a square pyramid. The square base of the pyramid has a side length of 6 meters, and each triangular face has a slant height of 11 meters. Ava needs to cover the entire roof (all four triangular faces and the square base) with weatherproof shingles. What is the total surface area of the roof in square meters? Answer: 168 Solution: Calculate the area of the square base. The base is a square with side length 6 meters. Area of square = side × side = 6 × 6 = 36 square meters.
    Full step-by-step solution

    Step 1: Calculate the area of the square base. The base is a square with side length 6 meters. Area of square = side × side = 6 × 6 = 36 square meters. Step 2: Calculate the area of one triangular face. Each triangle has a base of 6 meters (the side of the square) and a slant height of 11 meters. Area of triangle = (1/2) × base × slant height = (1/2) × 6 × 11 = 3 × 11 = 33 square meters. Step 3: Since there are 4 identical triangular faces, total area of the triangles = 4 × 33 = 132 square meters. Step 4: Add the base area and the triangular faces area: Total surface area = 36 + 132 = 168 square meters. The total surface area of the roof is 168 square meters.

  2. Aroha is painting a cylindrical storage tank. The tank has a radius of 9 cm and a height of 15 cm. What is the total surface area of the tank? (Use π = 3.14) Answer: 1356.48 Solution: Identify the formula for the surface area of a cylinder: SA = 2πr² + 2πrh. Calculate the area of the two circular bases: 2πr² = 2 × 3.14 × 9² = 2 × 3.14 × 81 = 2 × 254.34 = 508.68 cm².
    Full step-by-step solution

    Step 1: Identify the formula for the surface area of a cylinder: SA = 2πr² + 2πrh. Step 2: Calculate the area of the two circular bases: 2πr² = 2 × 3.14 × 9² = 2 × 3.14 × 81 = 2 × 254.34 = 508.68 cm². Step 3: Calculate the area of the curved side: 2πrh = 2 × 3.14 × 9 × 15 = 2 × 3.14 × 135 = 2 × 423.9 = 847.8 cm². Step 4: Add the two areas together: 508.68 + 847.8 = 1356.48 cm². The total surface area of the tank is 1356.48 cm².

  3. A cylinder has a radius of 14 cm and a height of 25 cm. Calculate its total surface area. (Use π = 22/7) Answer: 3432 Solution: Identify the given values: radius r = 14 cm, height h = 25 cm, π = 22/7. Calculate the area of the two circular ends. Area of one circle = πr² = (22/7) × 14² = (22/7) × 196 = 22 × 28 = 616 cm².
    Full step-by-step solution

    Step 1: Identify the given values: radius r = 14 cm, height h = 25 cm, π = 22/7. Step 2: Calculate the area of the two circular ends. Area of one circle = πr² = (22/7) × 14² = (22/7) × 196 = 22 × 28 = 616 cm². Two circles: 2 × 616 = 1232 cm². Step 3: Calculate the curved surface area. Curved surface area = 2πrh = 2 × (22/7) × 14 × 25 = 2 × 22 × 2 × 25 = 44 × 50 = 2200 cm². Step 4: Add the areas together: total surface area = 1232 + 2200 = 3432 cm². The total surface area is 3432 cm².

  4. Liam is designing a rectangular prism-shaped fish tank for his science project. The tank will be 2.5 meters long, 1.8 meters wide, and 1.2 meters high. He needs to calculate the total surface area to determine how much glass he needs to buy. What is the total surface area of the fish tank in square meters? Answer: 19.32 Solution: A rectangular prism has 6 faces. For Liam's fish tank, the dimensions are: Length L = 2.5 m Width W = 1.8 m Height H = 1.2 m The total surface area is the sum of the areas of all 6 faces.
    Full step-by-step solution

    A rectangular prism has 6 faces. For Liam's fish tank, the dimensions are: Length L = 2.5 m Width W = 1.8 m Height H = 1.2 m The total surface area is the sum of the areas of all 6 faces. There are three pairs of identical faces: 1. Top and Bottom faces: Each is a rectangle with area L × W. Area of one = 2.5 × 1.8 = 4.5 Since there are two (top and bottom), total for this pair = 2 × 4.5 = 9.0 2. Front and Back faces: Each is a rectangle with area L × H. Area of one = 2.5 × 1.2 = 3.0 Since there are two (front and back), total for this pair = 2 × 3.0 = 6.0 3. Left and Right faces: Each is a rectangle with area W × H. Area of one = 1.8 × 1.2 = 2.16 Since there are two (left and right), total for this pair = 2 × 2.16 = 4.32 Now, add the areas of all three pairs to get the total surface area: Total Surface Area = 9.0 + 6.0 + 4.32 = 19.32 Therefore, the total surface area of the fish tank is 19.32 square meters.