Surface Area of Prisms
Grade 7 · Math · Geometry · Alaska, USA
Lesson Summary
Calculate the total surface area of rectangular and triangular prisms.
Explanation
Surface area is the total area of every face of a three-dimensional shape. For a rectangular prism, add the areas of all six faces: SA = 2lw + 2lh + 2wh. For a triangular prism, find the area of the two triangular bases and the three rectangular sides, then add them together. Thinking of a 'net'—the shape unfolded flat—helps you see every face clearly.
Practice Questions
Q1: Find the surface area of a rectangular prism that is 4 cm long, 3 cm wide, and 5 cm tall.
Answer: SA = 2(4×3) + 2(4×5) + 2(3×5) = 24 + 40 + 30 = 94 cm².
Q2: A triangular prism has a triangular base with base 6 cm and height 4 cm. The prism is 10 cm long and the three rectangular faces have widths of 6 cm, 5 cm, and 5 cm. Find the surface area.
Answer: Two triangles: 2 × ½ × 6 × 4 = 24. Three rectangles: (6×10) + (5×10) + (5×10) = 60 + 50 + 50 = 160. Total SA = 24 + 160 = 184 cm².
Q3: A cube has edges of 7 in. What is its surface area?
Answer: A cube has 6 identical faces: SA = 6 × 7² = 6 × 49 = 294 in².
People Also Ask
What is Surface Area of Prisms in Grade 7 Math?+
Surface Area of Prisms is a lesson in the Geometry chapter of Grade 7 Math. It is part of the Alaska, USA school curriculum and covers key concepts that students need to understand at this level.
What grade level covers Surface Area of Prisms?+
Surface Area of Prisms is taught in Grade 7 as part of the Math curriculum in Alaska, USA.
How can I help my child with Geometry in Math?+
Start with the lesson summary and explanation on this page. Practice the questions provided, then use TutorTom for personalized, step-by-step help with Geometry topics.