Surface Area & Volume

Step 01 of 04

A net is a 2D pattern that folds up into a 3D shape. The TOTAL AREA of the net = surface area of the 3D shape.

Step 02 of 04

Rectangular prism (box) net. 6 rectangles in 3 matching pairs: top/bottom, front/back, left/right.

Step 03 of 04

Triangular prism net. 2 triangular ends + 3 rectangular sides. Compute each piece's area, sum them.

Step 04 of 04

Find a missing dimension by reverse-engineering. Given total surface area and known dimensions, you can solve for an unknown side.

Step 01 of 04

Volume formula stays the same:

Even when dimensions are fractions or decimals, just multiply.

Step 02 of 04

Worked example. Prism with length 3 1/2, width 2, height 4.

Step 03 of 04

All-fraction example. 1/2 × 1/3 × 1/4.

Step 04 of 04

Finding a fractional dimension. Given volume and two dimensions, divide.

Volume = 60 cubic ft, length = 5, width = 4. Height = $60/(5\times 4)=60/20=3$ ft.