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Finding Perimeter, Area, Volume, and Surface Area Study Guide: GED Math (page 3)

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Updated on Mar 23, 2011

Practice problems for these concepts can be found at:

Geometry Practice Problems: GED Math

Polygons

Plane figures are two-dimensional objects that reside on a plane. You can think of a plane like a sheet of paper that extends forever in all directions. Special figures are called polygons.

A good grasp of geometry requires a knowledge of the basic polygon shapes. Study the following geometry vocabulary.

A polygon is a closed plane figure made up of line segments.

A triangle is a polygon with three sides.

A quadrilateral is a polygon with four sides.

A pentagon is a polygon with five sides.

A hexagon is a polygon with six sides.

A heptagon or a septagon is a polygon with seven sides.

An octagon is a polygon with eight sides.

A quadrilateral with one pair of parallel sides (bases) is called a trapezoid. In an isosceles trapezoid, the sides that are not bases are congruent (equal in measure). Because the parallel bases are not the same length in a trapezoid, we call these bases b1 and b2.

A quadrilateral with two pairs of parallel sides is called a parallelogram. The two sets of opposite sides that are parallel are equal and congruent in a parallelogram, as shown in the diagram:

Parallelograms are broken down into further subgroups.

• A rectangle is a parallelogram with four right angles.
• A rhombus is a parallelogram with four equal and congruent sides.
• A square is a parallelogram with both four right angles and four equal and congruent sides. A square is a rhombus, a rectangle, a parallelogram, and a quadrilateral.

Finding Perimeter and Circumference

The GED provides you with several geometrical formulas. One of these is for the perimeter. Perimeter is the distance around a figure. You can calculate the perimeter of a figure by adding up the lengths of all the sides.

Example

Find the perimeter of a square whose side is 5 cm.

You know that each side of a square is equal. So, if you know that one side of a square is 5 cm, then you know that each side of the square is 5 cm. To calculate the perimeter, add up the lengths of all four sides.

5 + 5 + 5 + 5 = 20

So, the perimeter of a square whose side measures 5 cm is 20 cm.

The perimeter of a circle is called its circumference. You can calculate a circle's circumference using either its radius or its diameter.

The diameter is a line segment that goes through the center of a circle. The endpoints of the diameter are on the curve of the circle. Any line that begins at the center of a circle and ends on a point on the circle is called a radius. A circle's diameter is twice as long as its radius. So, if you know either the radius or the diameter, you can easily find the other.

To calculate circumference, use either of these formulas, where π = 3.14 ( π is a Greek symbol, spelled pi, and pronounced "pie"), d is the circle's diameter, and r is the circle's radius:

C = πd

C = 2πr

Example

Find the circumference of a circle with a diameter of 5 inches.

Because you know the diameter, use the formula that includes the diameter:

C = πd

C = π(5)

= (3.14)(5)

= 15.7

The final answer is 15.7 inches.

Finding Area

Area is a measure of the surface of a two-dimensional figure. The following table shows how to calculate the area of different figures.

Finding Volume

Volume is a measure of the amount of space inside a three-dimensional shape. Three-dimensional shapes are sometimes called solids.

The formula for calculating the volume of a rectangular solid is:

V = Ah

where V = the volume

A = the area of the base

h = the height

Examples
1. Find the volume of a cube that is 3 inches long on each edge.
2. Choose the correct formula. The problem tells you that you are measuring the volume of a cube. The formula for the volume of a cube is V = Ah or V = s3.

Plug in the known measures and solve:

V = 33

= 3 × 3 × 3

= 27

So the final answer is 27 square inches.

3. Find the volume of a cylinder that has a height of 10 cm and a radius of 5 cm.
4. Choose the correct formula. The problem tells you that you are measuring the volume of a cylinder. The formula for the volume of a cylinder is V = Ah or V = πr2h.

Plug in the known measures and solve:

V = πr2h

= π(5)2(10)

= π(25)(10)

= π(250)

= 785

So the final answer is 785 cubic centimeters.

(Cubic centimeters can also be written as cm3.)

Surface Area

The surface area of a three-dimensional object measures the area of each of its faces and adds them together. The total surface area of a rectangular solid is double the sum of the areas of the three different faces. For a cube, simply multiply the surface area of one of its sides by 6.

Practice problems for these concepts can be found at:

Geometry Practice Problems: GED Math