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GED Math : Area of a Quadrilateral

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Example Question #355 : Geometry And Graphs

Find the area of a square with a width of 7cm.

Possible Answers:

$49\text{cm}^2$

$\text{There is not enough information to solve the problem.}$

$42\text{cm}^2$

$35\text{cm}^2$

$28\text{cm}^2$

Correct answer:

$49\text{cm}^2$

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, we know the width of the square is 7cm. Because it is a square, all sides are equal. Therefore, the length is also 7cm. So, we can substitute. We get

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

$A = 49\text{cm}^2$

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Example Question #61 : Squares, Rectangles, And Parallelograms

Find the area of a rectangle with a length of 6in and a width that is a third of the length.

Possible Answers:

$12\text{in}^2$

$18\text{in}^2$

$24\text{in}^2$

$16\text{in}^2$

$9\text{in}^2$

Correct answer:

$12\text{in}^2$

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 6in. We also know the width of the triangle is a third of the length. Therefore, the width is 2in. So, we substitute. We get

$A = 6\text{in} \cdot 2\text{in}$

$A = 12\text{in}^2$

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Example Question #357 : Geometry And Graphs

A square has an area of $144\text{cm}^2$ . Find the length of one side.

Possible Answers:

$15\text{cm}$

$13\text{cm}$

$12\text{cm}$

$16\text{cm}$

$18\text{cm}$

Correct answer:

$12\text{cm}$

Explanation:

A square has 4 equal sides. The formula to find the area of a square is

A = b^2

where b is the length of one side of the square. To find the length of one side of the square, we will solve for b.

Now, we know the area of the square is $144\text{cm}^2$ . So, we will substitute and solve for b. So,

$144\text{cm}^2 = b^2$

$\sqrt{144\text{cm}^2} = \sqrt{b^2}$

$12\text{cm} = b$

$b = 12\text{cm}$

Therefore, the length of one side of the square is 12cm.

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Example Question #358 : Geometry And Graphs

Use the following rectangle to answer the question:

Rectangle1

Find the area.

Possible Answers:

$12\text{in}^2$

$9\text{in}^2$

$15\text{in}^2$

$24\text{in}^2$

$18\text{in}^2$

Correct answer:

$18\text{in}^2$

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.

So, given the rectangle

Rectangle1

we can see the length is 6in and the width is 3in. So, we can substitute. We get

$A = 6\text{in} \cdot 3\text{in}$

$A = 18\text{in}^2$

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Example Question #359 : Geometry And Graphs

Use the following square to answer the question:

Square2

Find the area.

Possible Answers:

$94\text{cm}^2$

$121\text{cm}^2$

$196\text{cm}^2$

$48\text{cm}^2$

$169\text{cm}^2$

Correct answer:

$196\text{cm}^2$

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

Square2

we can see the length is 14cm. Because it is a square, all sides are equal. Therefore, the width is also 14cm. So, we can substitute. We get

$A = 14\text{cm} \cdot 14\text{cm}$

$A = 196\text{cm}^2$

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Example Question #360 : Geometry And Graphs

Find the area of a square with a perimeter of .

Possible Answers:

256

128

2048

4096

Correct answer:

256

Explanation:

A square has four equal sides.

This means that each side is one fourth of the perimeter.

$s=\frac{1}{4} (64) = 16$

Write the area of a square.

A=s^2 = 16^2 = 256

The answer is: 256

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Example Question #361 : Geometry And Graphs

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

Possible Answers:

8x+4

16x^2+8x+1

8x^2+4x+1

8x+1

16x^2+1

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 #362 : Geometry And Graphs

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

Possible Answers:

$121\text{in}^2$

$110\text{in}^2$

$111\text{in}^2$

$132\text{in}^2$

$144\text{in}^2$

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 #361 : 2 Dimensional Geometry

Use the following rectangle to answer the question:

Rectangle4

Find the area.

Possible Answers:

$32\text{cm}^2$

$72\text{cm}^2$

$16\text{cm}^2$

$54\text{cm}^2$

$63\text{cm}^2$

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 #361 : 2 Dimensional Geometry

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

Possible Answers:

$96\text{in}^2$

$72\text{in}^2$

$36\text{in}^2$

$54\text{in}^2$

$18\text{in}^2$

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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GED Math : Area of a Quadrilateral

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #355 : Geometry And Graphs

Example Question #61 : Squares, Rectangles, And Parallelograms

Example Question #357 : Geometry And Graphs

Example Question #358 : Geometry And Graphs

Example Question #359 : Geometry And Graphs

Example Question #360 : Geometry And Graphs

Example Question #361 : Geometry And Graphs

Example Question #362 : Geometry And Graphs

Example Question #361 : 2 Dimensional Geometry

Example Question #361 : 2 Dimensional Geometry

All GED Math Resources

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