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# Geometry for Nursing School Entrance Exam Study Guide (page 3)

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Updated on Aug 12, 2011

### Perimeter

Shortcut: Take advantage of the fact that the opposite sides of a rectangle and a parallelogram are equal: Just add two adjacent sides and double the sum. Similarly, multiply one side of a square by four.

### Area

To find the area of a rectangle, square, or parallelogram, use this formula:

The base is the size of one of the sides. It is easiest if you call the side on the bottom the base, but any side can be a base. The height (or altitude) is the size of a perpendicular line drawn from the base to the side opposite it. The height of a rectangle and a square is the same as the size of its non-base side.

Caution: A parallelogram's height is not usually the same as the size connecting the base to its opposite side (called the slant height), but the size of a perpendicular line drawn from the base to the side opposite it.

Example: Find the area of a rectangle with a base of 4 meters and a height of 3 meters.

1. Draw the rectangle as close to scale as possible.
2. Label the size of the base and height.
3. Write the area formula; then substitute the base and height numbers into it: Thus, the area is 12 square meters.

### Circles

We can all recognize a circle when we see one, but its definition is a bit technical. A circle is a set of points that are all the same distance from a given point called the center. That distance is called the radius. The diameter is twice the length of the radius; it passes through the center of the circle.

### Circumference

The circumference of a circle is the distance around the circle (it is the perimeter of the circle). To determine the circumference of a circle, use either of these two equivalent formulas:

• d is the diameter (which is the same as 2x the radius)
• π is approximately equal (denoted by the symbol ) to 3.14 or

Note: Math often uses letters of the Greek alphabet, like π (pi). Perhaps that's what makes math seem like Greek to some people! In the case of the circle, you can use π as a hint to recognize a circle question: A pie is shaped like a circle.

Example: Find the circumference of a circle whose radius is 7 inches.

1. Draw this circle and write the radius version of the circumference formula (because you're given the radius):
2. Substitute 7 for the radius:
3. On a multiple-choice test, look at the answer choices to determine whether to leave π in your answer or substitute the value of π in the formula. If the answer choices don't include π, substitute or 3.14 for π and multiply:
If the answer choices include π, just multiply:

All the answers—44 inches, 43.96 inches, and 14π inches—are considered correct.

Example: What is the diameter of a circle with a circumference of 62.8 centimeters? Use 3.14 for π.

1. Draw a circle with its diameter and write the diameter version of the circumference formula (because you're asked to find the diameter):
2. Substitute 62.8 for the circumference, 3.14 for π, and solve the equation:
62.8 = 3.14 × d
62.8 = 3.14 × 20
3. The diameter is 20 centimeters.

### Area

The area of a circle is the space its surface occupies. To determine the area of a circle, use this formula:

Hint: To avoid confusing the area and circumference formulas, just remember that area is always measured in square units, like 12 square yards of carpeting. Thus, the area formula is the one with the squared term in it.

Example: Find the area of the circle at right, rounded to the nearest tenth:

1. Write the area formula:
2. Substitute 2.3 for the radius:
3. On a multiple-choice test, look at the answer choices to determine whether to use π or an approximate value of π (decimal or fraction) in the formula. If the answers don't include π, use 3.14 for π (because the radius is a decimal):
4. If the answers include π, multiply and round:

Both answers—16.6 square inches and 5.3π square inches—are correct.

Example: What is the diameter of a circle with an area of 9π square centimeters?

1. Draw a circle with its diameter (to help you remember that the question asks for the diameter); then write the area formula:
2. Substitute 9π for the area and solve the equation:

Since the radius is 3 centimeters, the diameter is 6 centimeters.

The practice quiz for this study guide can be found at: