ASVAB Mathematics Knowledge Practice: Irregular and Composite Shapes

On the Mathematics Knowledge subtest on the ASVAB, not all shape problems will be about simple squares and circles. Some will involve irregular shapes, or even composite shapes (multiple shapes combined into one).

Although the following practice questions may look a little intimidating, once you start to work on them, you'll see they're pretty straightforward.

Practice questions

1. Find the perimeter:

   

   A. 67 m B. 38 m C. 68 m D. 75 m

2. Find the area:

   

   A. 81 m² B. 47 m² C. 75 m² D. 78 m²

Answers and explanations

1. The correct answer is Choice (A).

   It doesn't matter what irregular shape you're dealing with when you find perimeter. You simply add the lengths of the sides:

   P = 20 + 7 + 10 + 9 + 21 = 67

2. The correct answer is Choice (D).

   One approach is to divide the figure into three rectangles and then add the areas together to find the total area.

   

   Use the formula A = lw, with l representing length and w representing width, to find the area of each rectangle. The first rectangle is 6 m by 9 m:

   A = 6(9) = 54

   The second rectangle is 3 m by 2 m (which is 9 m – 7 m):

   A = 3(2) = 6

   And the third rectangle is 2 m by 9 m:

   A = 2(9) = 18

   Add the areas to get the total:

   A = 54 + 6 + 18 = 78

   Another option is to calculate the area as if you were dealing with just one, whole rectangle and then subtract the missing part:

   

   The whole area is

   

   The area of the missing rectangle is A = 7(3) = 21

   Subtract: