7th Grade Pre-Algebra: Help with Area and Volume

Area and Volume for 7th Graders

Students usually learn about area and volume in geometry class, but these can also be considered pre-algebra skills because they require you to solve for a variable. For instance, if you're finding the area of a rectangle, you'll solve the equation A = length x width for the variable 'A.' Alternatively, you might be asked to solve for the rectangle's length when given its area and its width.

Area and Surface Area

Many 7th graders have already learned the area formulas for most 2-dimensional shapes, but some schools introduce the formula for the area of a circle in 7th grade. The formula is A = (pi)r^2, where 'r' is the radius (half the diameter), and the value of 'pi' is 3.14.

The surface area for any regular, 3-dimensional object, like a cylinder or rectangular prism, is equal to the sum of the areas of its surfaces. For instance, a rectangular prism has two smaller bases and four larger sides. To find the total surface area, add together the areas of the two small bases. Then, add the sum of the areas of the four large bases. Here's one common way to write this formula, where 'l' is length, 'w' is width and 'h' is height:

V = 2(l x w) + 2(l x h) + 2(w x h)

Volume

A regular, 3-dimensional object's volume is the product of the area of its base and its height. Returning to the rectangular prism example in the last section, you would multiply the area of one of the small bases by the height of the prism to get its volume. This formula can be written as V = l x w x h, since the area of the base is equal to length times width (l x w). For a cube, the formula is V = s^3, where 's' is the length of a side.

To find the volume of a cylinder, calculate the area of the circular base using the formula given in the first section, A = (pi)r^2. Then, multiply this by the height of the cylinder, 'h.' Putting this all together, the formula is V = (pi)r^2 * h.

The volume of a triangular prism is the product of the prism's height, 'h,' and the area of its base (V = Height * Area of the Base). You can find the area of the prism's triangular base using the formula A = 1/2 * b * h, where 'b' is the base of the triangle and 'h' is its height. Be careful not to confuse the height of the triangle with the height of the prism, or the area of the prism's base with the length of the triangle's base.