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GED Math : Geometry and Graphs

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 #21 : Area Of A Quadrilateral

Find the area of a square with a perimeter of 16x+4 .

Possible Answers:

8x^2+4x+1

8x+1

16x^2+8x+1

16x^2+1

8x+4

Correct answer:

16x^2+8x+1

Explanation:

To find the length of one side, we will need to divide the perimeter by 4, since a square has four equal sides.

$\frac{16x+4}{4} = 4x+1$

The area of a square is: s^2

Square the quantity of the side.

(4x+1)^2 = (4x+1)(4x+1)

Use the FOIL method to solve.

(4x)(4x)+(4x)(1)+ (1)(4x)+(1)(1)

16x^2+4x+4x+1 = 16x^2+8x+1

The answer is: 16x^2+8x+1

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Example Question #22 : Area Of A Quadrilateral

Find the area of a square with a width of 11in.

Possible Answers:

$121\text{in}^2$

$144\text{in}^2$

$111\text{in}^2$

$110\text{in}^2$

$132\text{in}^2$

Correct answer:

$121\text{in}^2$

Explanation:

To find the area of a square, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the square.

Now, we know the width of the square is 11in. Because it is a square, all sides are equal. Therefore, the length is also 11in.

So, we will substitute. We get

$A = 11\text{in} \cdot 11\text{in}$

$A = 121\text{in}^2$

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Example Question #23 : Area Of A Quadrilateral

Use the following rectangle to answer the question:

Rectangle4

Find the area.

Possible Answers:

$16\text{cm}^2$

$54\text{cm}^2$

$32\text{cm}^2$

$63\text{cm}^2$

$72\text{cm}^2$

Correct answer:

$63\text{cm}^2$

Explanation:

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, given the rectangle

Rectangle4

we can see the length is 9cm and the width is 7cm. So, we will substitute. We get

$A = 9\text{cm} \cdot 7\text{cm}$

$A = 63\text{cm}^2$

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Example Question #24 : Area Of A Quadrilateral

Find the area of a rectangle with a length of 12in and a width that is half the length.

Possible Answers:

$72\text{in}^2$

$18\text{in}^2$

$36\text{in}^2$

$96\text{in}^2$

$54\text{in}^2$

Correct answer:

$72\text{in}^2$

Explanation:

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 12in. We know the width of the rectangle is half the length. Therefore, the width is 6in. Now, we can substitute. We get

$A = 12\text{in} \cdot 6\text{in}$

$A = 72\text{in}^2$

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Example Question #31 : Area Of A Quadrilateral

What is the area of a square with a perimeter of ?

Possible Answers:

$\frac{9}{16}$

$\frac{9}{8}$

$\frac{9}{2}$

$\frac{9}{4}$

Correct answer:

$\frac{9}{16}$

Explanation:

The perimeter includes the sum of the four sides of the square.

4s=3

Divide by 4 on each side.

$s=\frac{3}{4}$

Each side has a length of three fourths.

Write the formula for the area of a square.

A=s^2

Substitute the side.

$A= (\frac{3}{4})^2 = (\frac{3}{4}) (\frac{3}{4}) = \frac{9}{16}$

The area is: $\frac{9}{16}$

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Example Question #32 : Area Of A Quadrilateral

Find the area of a rectangle with a length of and a height of 4x^2 .

Possible Answers:

32 x^3

32 x^2

24x^3

16x^3

24x^2

Correct answer:

32 x^3

Explanation:

Write the formula to find the area of a rectangle.

A = LW

Substitute the dimensions.

A = (8x)(4x^2) = 32 x^3

The answer is: 32 x^3

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Example Question #33 : Area Of A Quadrilateral

What is the area of a square with a side of $3\sqrt5$ ?

Possible Answers:

Correct answer:

Explanation:

Write the area formula for a square.

A = s^2

Substitute the side length in the equation.

$A = (3\sqrt5)^2 = (3\sqrt5) (3\sqrt5) = 9(5) = 45$

The area is:

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Example Question #34 : Area Of A Quadrilateral

What is the area of a square that has a perimeter of 154.2 ?

Possible Answers:

5944.4

77.1

1486.1

1322.4

Correct answer:

1486.1

Explanation:

Start by finding the length of a side for the square by using the given perimeter.

$\text{Perimeter}=4(\text{side})$

$\text{side}=\frac{\text{Perimeter}}{4}$

For the given square,

$\text{side}=\frac{154.2}{4}=38.55$

Now, recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Plug in the side length of the square to find its area.

$\text{Area}=(38.55)^2=1486.1$

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Example Question #35 : Area Of A Quadrilateral

Use the following rectangle to answer the question:

Rectangle4

Find the area.

Possible Answers:

$32\text{cm}^2$

$63\text{cm}^2$

$54\text{cm}^2$

$16\text{cm}^2$

$72\text{cm}^2$

Correct answer:

$63\text{cm}^2$

Explanation:

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, given the rectangle

Rectangle4

we can see the length is 9cm and the width is 7cm. So, we substitute. We get

$A = 9\text{cm} \cdot 7\text{cm}$

$A = 63\text{cm}^2$

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Example Question #36 : Area Of A Quadrilateral

Use the following square to answer the question:

Square3

Find the area.

Possible Answers:

$64\text{cm}^2$

$24\text{cm}^2$

$56\text{cm}^2$

$32\text{cm}^2$

$16\text{cm}^2$

Correct answer:

$64\text{cm}^2$

Explanation:

To find the area of a square, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the square.

Now, given the square

Square3

we can see the width is 8cm. Because it is a square, all sides are equal. Therefore, the length is also 8cm. So, we can substitute. We get

$A = 8\text{cm} \cdot 8\text{cm}$

$A = 64\text{cm}^2$

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Area Of A Quadrilateral

Example Question #22 : Area Of A Quadrilateral

Example Question #23 : Area Of A Quadrilateral

Example Question #24 : Area Of A Quadrilateral

Example Question #31 : Area Of A Quadrilateral

Example Question #32 : Area Of A Quadrilateral

Example Question #33 : Area Of A Quadrilateral

Example Question #34 : Area Of A Quadrilateral

Example Question #35 : Area Of A Quadrilateral

Example Question #36 : Area Of A Quadrilateral

All GED Math Resources

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