### All GRE Math Resources

## Example Questions

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

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

**Possible Answers:**

18

9

40.5

36

**Correct answer:**

36

36

A square has four equal sides and its area = side^{2}. 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 #1 : Squares

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

**Possible Answers:**

**Correct answer:**

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 #2 : Squares

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:**

16

20π

16 + 2π

None of the other answers

12 + 2π

**Correct answer:**

12 + 2π

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

Instead of solving the algebra, you should immediately note several things. 16 = 4^{2} and 4 = 2^{2}. 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 #3 : Squares

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:**

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 #4 : Squares

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

**Possible Answers:**

**Correct answer:**

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 .

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