Geometric problems on the ASVAB require you to compute the volume, perimeter, area, circumference, diameter, and so on of various geometric shapes. These problems are not very difficult with a little knowledge of some geometric formulas.

You’re painting a fence that is 20 feet long and 6 feet high. How much square footage of fence are you covering with paint?

The area formula for a rectangle is a = lw, so the answer to this simple problem is a = 6 × 20 = 120 square feet.

Generally, the Arithmetic Reasoning test makers don’t let you off so easy, though. The problem is more likely to be written something like the following.

You’re painting a fence that is 20 feet long and 6 feet high. Paint costs $7.23 per gallon, and 1 gallon of paint covers 60 square feet of fence. How much do you need to spend on paint to complete the project?

The problem now requires a couple of extra steps to answer. First, you have to compute the area of the fence. You already did that: 120 square feet.

Now you have to determine how many gallons of paint you need to buy to cover 120 square feet. Because 1 gallon of paint covers 60 square feet, you need 120 ÷ 60 = 2 gallons of paint.

Finally, you need to figure how much 2 gallons of paint cost. Paint is $7.23 per gallon, and you need 2 gallons, so $7.23 × 2 = $14.46.

You get quite a few geometric problems on the Arithmetic Reasoning subtest. To make sure you’re ready for them, memorize these basic geometric formulas.

Shape Function Formula
Square Area a = s2
Perimeter p = 4s
Rectangle Area a = lw
Perimeter p = 2l + 2w
Triangle Perimeter p = s1 + s2 + s3
Area a=1/2bh
Right Triangle Pythagorean theorem a2 + b2 = c2
Circle Radius r=1/2d
Diameter d = 2r
Circumference c = 2ðr
Area a = ðr2
Cube Volume v = s3
Surface Area SA = 6s2
Rectangular Box Volume v = lwh
Surface Area SA = 2lw + 2wh + 2lh
Cylinder Volume v = ðr2h