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How to Solve Geometric Problems on the ASVAB

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
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