GRE Math : How to find the perimeter of a square

Study concepts, example questions & explanations for GRE Math

varsity tutors app store varsity tutors android store varsity tutors amazon store varsity tutors ibooks store

Example Questions

Example Question #1 : Squares

What is the perimeter of a square that has an area of 81?

Possible Answers:

40.5

9

18

36

Correct answer:

36

Explanation:

36

A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:

4 * 9 = 36 

Example Question #45 : Quadrilaterals

Geometry_2

The radius of the circle is 2 inches. What is the perimeter of the inscribed square? 

Possible Answers:

Correct answer:

Explanation:

The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be  .

Finally, the perimeter of a square is

Example Question #1 : How To Find The Perimeter Of A Square

Semicirclesquare

The diagram above represents a square ABCD with a semi-circle directly attached to its side.  If the area of the figure is 16 + 2π, what is its outer perimeter?

Possible Answers:

12 + 2π

20π

16 + 2π

16

None of the other answers

Correct answer:

12 + 2π

Explanation:

We know that our area can be represented by the following equation:

Instead of solving the algebra, you should immediately note several things.  16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:

 which is just what we need.

With s = 4, we know that 3 sides of our figure will have a perimeter of 12.  The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.

Therefore, the outer perimeter of our figure is 12 + 2π.

Example Question #2 : How To Find The Perimeter Of A Square

A square table has an area of  square centimeters and a perimeter of  centimeters.

If , what is the perimeter of the square?

Possible Answers:

Correct answer:

Explanation:

We start by writing the equations for the area and perimeter in terms of a side of length s.

Then, substitute both of these expressions into the given equation to solve for side length.

Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.

Example Question #48 : Quadrilaterals

The diagonal of square  is  feet. Approximately how long in inches is the perimeter of square ?

Possible Answers:

Correct answer:

Explanation:

First we must convert to inches.

The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that , where x is equal to the length of one side of the square.

This gives us .

Therefore, the perimeter of square  is equal to .

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: