7.G.6: Area, Volume and Surface Area Problems
Also written as 7.G.B.6 and CCSS.MATH.CONTENT.7.G.B.6 · Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
The Official Wording
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Common Core State Standards, Grade 7, Geometry · Read it at the source · Checked October 14, 2026
What 7.G.6 Means in Plain English
Seventh graders find area, surface area and volume for objects built from simple pieces. A tent shaped like a triangular prism, with ends 6 ft wide and 4 ft tall, 8 ft long, holds 12 × 8 = 96 ft³, and its five faces total 152 ft² of fabric.
The real skill is choosing the measure the question needs and breaking the object into faces or blocks. In 8th grade the same base-times-height idea reaches cylinders, cones and spheres (8.G.9), and high school adds pyramids with V = ⅓Bh (HSG-GMD.3).
7.G.6 I Can Statements
- I can find the volume of a prism as base area times length.
- I can find surface area by adding the areas of every face.
- I can split a composite shape into pieces I can measure.
7.G.6 Worked Example
A pup tent asks both questions at once: how much air is inside, and how much fabric it takes, floor included.
A pup tent is a triangular prism 8 ft long. Each triangular end is 6 ft wide at the bottom and 4 ft tall, and each sloping side is 5 ft from ground to ridge. How much space is inside, and how much fabric covers it, floor included?
- The prism is named for the triangle at each end, so that triangle is the base, not the floor.Base area = ½ × 6 × 4 = 12 ft²
- Volume of a right prism is base area times the length between the two bases.V = 12 × 8 = 96 ft³
- For surface area, list every face. Start with the two triangle ends.2 × 12 = 24 ft²
- Then the two sloping rectangles, 5 ft by 8 ft, and the floor, 6 ft by 8 ft.2 × (5 × 8) + 6 × 8 = 80 + 48 = 128 ft²
- Add all five faces.SA = 24 + 128 = 152 ft²
Check it: The tent is half of a 6 by 4 by 8 ft box, which holds 6 × 4 × 8 = 192 ft³, and half of 192 is 96. A triangular prism has 5 faces, and the list has 2 ends, 2 sides and 1 floor.
Common Mistakes with 7.G.6
Using the floor as the base
V = 6 × 8 × 4 = 192 ft³
Try this: Find the two matching faces the prism is named for, here the triangle ends, and multiply that area by the distance between them.
Leaving out a face
SA = 24 + 80 = 104 ft², with no floor
Try this: List the faces before adding, then count them: a triangular prism has five, so a list of four is short one.
Mixing square and cubic units
The tent holds 152 ft²
Try this: Ask whether the answer fills or covers: filling is volume in cubic feet, covering is surface area in square feet.
Where 7.G.6 Fits
Practice 7.G.6
Quick Check
- A box is 5 cm by 4 cm by 3 cm. Find its volume and surface area.
- A prism’s base is a trapezoid with area 18 in², and the prism is 10 in long. What is its volume?
- An L-shaped patio is a 10 ft by 6 ft rectangle joined to a 4 ft by 3 ft rectangle. What is its area?