7th Grade Area, Volume and Surface Area Lesson (Free PDF)
This area volume surface area lesson for 7th Grade covers area, volume and surface area (Common Core 7.G.B.6), with a free PDF to print.
The area of a triangle is half the base times the height, and a trapezoid has area half the sum of its bases times the height. The volume of a right prism is the base area times the height. The surface area of a prism is the sum of the areas of all its faces, found from its net.
Grade 7 · Common Core State Standards: 7.G.B.6
Key facts in this area volume surface area lesson
- Triangle: \(A = \frac{1}{2} bh\). Trapezoid: \(A = \frac{1}{2} (b_1 + b_2) h\).
- Composite polygon: add the areas of simple pieces or subtract a missing piece.
- Volume of a prism: \(V = Bh\) (base area times height).
- Surface area of a prism: add the areas of all faces from the net.
- Area uses square units; volume uses cubic units.
How do you find the area of triangles and quadrilaterals?
Each formula comes from the rectangle. The area of a rectangle is base times height, \(A = bh\). A parallelogram has the same formula with a perpendicular height. A triangle is half of a parallelogram.
| Shape | Area formula |
|---|---|
| Rectangle or parallelogram | \(A = bh\) |
| Triangle | \(A = \frac{1}{2} bh\) |
| Trapezoid | \(A = \frac{1}{2} (b_1 + b_2) h\) |
How do you find the area of a composite polygon?
Break the polygon into rectangles and triangles, find each area, and add. Or find the area of a bigger shape and subtract the missing part.
How do you find the volume of a right prism?
For a rectangular prism, \(B = l \times w\), so \(V = lwh\). For a triangular prism, \(B = \frac{1}{2} bh\) of the triangle, and the length of the prism plays the role of height.
How do you find the surface area of a prism?
The surface area is the total area of all faces. Draw the net and add the areas of the rectangles and other shapes. A box 6 by 4 by 3 has pairs of faces: \(2(6 \times 4) + 2(6 \times 3) + 2(4 \times 3) = 48 + 36 + 24 = 108\) square units.
Surface area is measured in square units and volume in cubic units, so always check the units in your final answer.
Area volume surface area lesson: questions and answers
What is the formula for the area of a triangle?
The area is half the base times the height, \(A = \frac{1}{2} bh\). The height must be perpendicular to the base.
How do you find the volume of a triangular prism?
Find the area of the triangular base, then multiply by the length of the prism. For a base of \(\frac{1}{2} (4)(3) = 6\) and length 10, the volume is 60.
What is surface area?
Surface area is the total area of all the faces of a solid. For a prism, draw the net and add the areas of every face.
How do I find the area of an L-shaped figure?
Split it into rectangles or subtract a missing rectangle from a larger one. Then add or subtract the areas.
What is the difference between volume and surface area?
Volume measures the space inside a solid in cubic units. Surface area measures the covering outside in square units.
How to use this area volume surface area lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the area volume surface area lesson as a PDF with the button below and keep it with your notes.
All Grade 7 chapters: Grade 7 math.
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