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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Other Shapes

Thingy

Refer to the above figure.

Which of the following segments is a diagonal of Pentagon KLMNO ?

Possible Answers:

$\overline{KM}$

$\overline{KQ}$

$\overline{NO}$

$\overline{RO}$

Correct answer:

$\overline{KM}$

Explanation:

A diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon. Of the four choices, only $\overline{KM}$ fits this description.

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Example Question #3 : Other Shapes

Octagon

Classify the above polygon.

Possible Answers:

Octagon

Hexagon

Pentagon

Rhombus

Correct answer:

Octagon

Explanation:

A polygon with eight sides is called an octagon.

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Example Question #395 : 2 Dimensional Geometry

Hexagon

Classify the above polygon.

Possible Answers:

Trapezoid

Pentagon

Hexagon

Octagon

Correct answer:

Hexagon

Explanation:

A polygon with six sides is called a hexagon.

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Example Question #2 : Other Shapes

Hexagon HEXAGO is regular. If diagonals $\overline{EO}$ and $\overline{XG}$ are constructed, which of the following classifications applies to Quadrilateral EXGO ?

I) Rectangle

II) Rhombus

III) Square

IV) Trapezoid

Possible Answers:

I only

II only

I, II, and III only

IV only

Correct answer:

I only

Explanation:

The figure described is below.

Hexagon

Since the hexagon is regular, its sides are congruent, and its angles each have measure $180 ^{\circ } \times \frac{6-2}{6} = 180 ^{\circ } \times \frac{4}{6} = 120^{\circ }$ .

Also, each of the triangles are isosceles, and their acute angles measure $\frac{1}{2} (180^{\circ }- 120^{\circ }) = 30^{\circ }$ each. This means that each of the four angles of Quadrilateral EXGO measures $120 ^{\circ }- 30^{\circ }= 90^{\circ }$ , so Quadrilateral EXGO is a rectangle. However, not all sides are congruent, so it is not a rhombus. Also, since it is a rectangle, it cannot be a trapezoid.

The correct response is I only.

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Example Question #4 : Perimeter And Sides

Octagon

The above figure is a regular octagon. Give its perimeter in yards.

Possible Answers:

$16 \frac{2}{3}\textrm{ yds}$

$20 \frac{5}{6}\textrm{ yds}$

$15\textrm{ yds}$

$12 \frac{1}{2}\textrm{ yds}$

Correct answer:

$16 \frac{2}{3}\textrm{ yds}$

Explanation:

A regular octagon has eight sides of equal length, so multiply the length of one side by eight:

$6 \frac{1}{4} \times 8 = \frac{25}{4} \times \frac{8}{1} = \frac{200}{4} = 50$ feet.

Divide by three to get the equivalent in yards:

$50 \div 3 = 16 \frac{2}{3}$ yards.

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Example Question #6 : Perimeter And Sides

What is the perimeter of a semicircle with an area of $16\pi$ ?

Possible Answers:

$4\pi \sqrt2$

$8\sqrt2+ 4\pi \sqrt2$

$4\sqrt2+ 4\pi \sqrt2$

$2\sqrt2+ 8\pi \sqrt2$

$16\sqrt2+ 8\pi \sqrt2$

Correct answer:

$8\sqrt2+ 4\pi \sqrt2$

Explanation:

Write the formula for the area of a semicircle.

$A = \frac{1}{2}\pi r^2$

Substitute the area.

$16\pi = \frac{1}{2}\pi r^2$

Multiply by 2, and divide by pi on both sides.

$\frac{16\pi \cdot (2)}{\pi}=\frac{ \frac{1}{2}\cdot (2)\pi r^2}{\pi}$

The equation becomes:

r^2 =32

Square root both sides and factor the right side.

$\sqrt{r^2} =\sqrt{32}$

$r=4\sqrt{2}$

The diameter is double the radius.

$D=8\sqrt{2}$

The circumference is half the circumference of a full circle.

$C_{semi}=\frac{1}{2}\pi D = 4\pi \sqrt{2}$

The perimeter is the sum of the diameter and the half circumference.

The answer is: $8\sqrt2+ 4\pi \sqrt2$

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Example Question #7 : Perimeter And Sides

A hexagon has a perimeter of 90in. Find the length of one side.

Possible Answers:

$22\text{in}$

$18\text{in}$

$20\text{in}$

$15\text{in}$

$9\text{in}$

Correct answer:

$15\text{in}$

Explanation:

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

P = 6a

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 90in. So, we will substitute and solve for a. We get

$90\text{in} = 6a$

$\frac{90\text{in}}{6} = \frac{6a}{6}$

$15\text{in} = a$

$a = 15\text{in}$

Therefore, the length of one side of the hexagon is 15in.

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Example Question #1362 : Ged Math

A hexagon has a perimeter of 138cm. Find the length of one side.

Possible Answers:

$18\text{cm}$

$19\text{cm}$

$22\text{cm}$

$21\text{cm}$

$23\text{cm}$

Correct answer:

$23\text{cm}$

Explanation:

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is

P = 6a

where a is the length of any side. To find the length of one side, we solve for a.

Now, we know the perimeter of the hexagon is 138cm. So, we can substitute and solve for a. We get

$138\text{cm} = 6a$

$\frac{138\text{cm}}{6} = \frac{6a}{6}$

$23\text{cm} = a$

$a = 23\text{cm}$

Therefore, the length of one side of the hexagon is 23cm.

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Example Question #11 : Perimeter And Sides

A hexagon has a perimeter of 126in. Find the length of one side.

Possible Answers:

$20\text{in}$

$18\text{in}$

$9\text{in}$

$22\text{in}$

$21\text{in}$

Correct answer:

$21\text{in}$

Explanation:

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

P = 6a

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 126in. So, we will substitute and solve for a. We get

$126\text{in} = 6a$

$\frac{126\text{in}}{6} = \frac{6a}{6}$

$21\text{in} = a$

$a = 21\text{in}$

Therefore, the length of one side of the hexagon is 21in.

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Example Question #11 : Other Shapes

A hexagon has a perimeter of 198cm. Find the length of one side.

Possible Answers:

$33\text{cm}$

$29\text{cm}$

$31\text{cm}$

$28\text{cm}$

$32\text{cm}$

Correct answer:

$33\text{cm}$

Explanation:

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is

P = 6a

where a is the length of any side. To find the length of one side, we solve for a.

Now, we know the perimeter of the hexagon is 198cm. So, we can substitute and solve for a. We get

$198\text{cm} = 6a$

$\frac{198\text{cm}}{6} = \frac{6a}{6}$

$33\text{cm} = a$

$a = 33\text{cm}$

Therefore, the length of one side of the hexagon is 33cm.

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #3 : Other Shapes

Example Question #3 : Other Shapes

Example Question #395 : 2 Dimensional Geometry

Example Question #2 : Other Shapes

Example Question #4 : Perimeter And Sides

Example Question #6 : Perimeter And Sides

Example Question #7 : Perimeter And Sides

Example Question #1362 : Ged Math

Example Question #11 : Perimeter And Sides

Example Question #11 : Other Shapes

All GED Math Resources

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