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GED Math : Area of a Quadrilateral

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Example Question #341 : 2 Dimensional Geometry

A rectangle has length 10 inches and width 8 inches. Its length is increased by 2 inches, and its width is decreased by 2 inches. By what percent has the area of the rectangle decreased?

Possible Answers:

$8 \%$

$10 \%$

$12 \frac{1}{2} \%$

$11 \frac{1}{9} \%$

Correct answer:

$10 \%$

Explanation:

The area of a rectangle is its length times its width.

Its original area is $10 \times 8 = 80$ square inches; its new area is $12 \times 6 = 72$ square inches. The area has decreased by

$\frac{80 -72}{80} \times 100 \% = \frac{8}{80} \times 100 \% = 10 \%$ .

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Example Question #342 : 2 Dimensional Geometry

A rectangle has length 10 inches and width 5 inches. Each dimension is increased by 3 inches. By what percent has the area of the rectangle increased?

Possible Answers:

$108 \%$

$58 \%$

$104 \%$

$54 \%$

Correct answer:

$108 \%$

Explanation:

The area of a rectangle is its length times its width.

Its original area is $10 \times 5 = 50$ square inches; its new area is $13 \times 8 = 104$ square inches. The area has increased by

$\frac{104 - 50}{50 } \times 100 = \frac{54}{50 } \times 100 = 108 \%$ .

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Example Question #343 : Geometry And Graphs

Find the area of a square with a side of 4x^2 .

Possible Answers:

16 x^4

$8\pi x^4$

$8\pi^2 x^2$

$8\pi x^2$

$16\pi^2 x^4$

Correct answer:

16 x^4

Explanation:

Write the formula for the area of a square.

A=s^2

Substitute the side into the equation.

A= (4x^2)^2

Simplify the equation.

The answer is: 16 x^4

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Example Question #344 : Geometry And Graphs

If a rectangle has a length of 18cm and a width that is half the length, what is the area of the rectangle?

Possible Answers:

$72\text{cm}^2$

$36\text{cm}^2$

$144\text{cm}^2$

$126\text{cm}^2$

$162\text{cm}^2$

Correct answer:

$162\text{cm}^2$

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, we know the length of the rectangle is 18cm. We also know the width is half the length. Therefore, the width is 9cm. So, we can substitute. We get

$A = 18\text{cm} \cdot 9\text{cm}$

$A = 162\text{cm}^2$

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Example Question #345 : Geometry And Graphs

If a square has a length of 10in, find the area.

Possible Answers:

$100\text{in}^2$

$125\text{in}^2$

$60\text{in}^2$

$40\text{in}^2$

$50\text{in}^2$

Correct answer:

$100\text{in}^2$

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 length of the square is 10in. Because it is a square, all sides are equal. Therefore, the length is also 10in. So, we can substitute. We get

$A = 10\text{in} \cdot 10\text{in}$

$A = 100\text{in}^2$

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Example Question #346 : Geometry And Graphs

Find the area of a rectangle with a width of 8in and a length that is two times the width.

Possible Answers:

$36\text{in}^2$

$64\text{in}^2$

$144\text{in}^2$

$128\text{in}^2$

$16\text{in}^2$

Correct answer:

$128\text{in}^2$

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 width of the rectangle is 8in. We also know the length of the rectangle is two times the width. Therefore, the length is 16in. So, we can substitute. We get

$A = 16\text{in} \cdot 8\text{in}$

$A = 128\text{in}^2$

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Example Question #351 : Geometry And Graphs

Find the area of a square with a length of 11cm.

Possible Answers:

$121\text{cm}^2$

$111\text{cm}^2$

$131\text{cm}^2$

$100\text{cm}^2$

$144\text{cm}^2$

Correct answer:

$121\text{cm}^2$

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 length of the square is 11cm. Because it is a square, all sides are equal. Therefore, the width is also 11cm. So, we can substitute. We get

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

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

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Example Question #352 : Geometry And Graphs

Find the area of a rectangle with a width of 7in and a length that is three times the width.

Possible Answers:

$21\text{in}^2$

$63\text{in}^2$

$28\text{in}^2$

$147\text{in}^2$

$168\text{in}^2$

Correct answer:

$147\text{in}^2$

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 width of the rectangle is 7in. We also know the length is three times the width. Therefore, the length is 21in. So, we can substitute. We get

$A =21\text{in} \cdot 7\text{in}$

$A = 147\text{in}^2$

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Example Question #353 : Geometry And Graphs

A square has an area of $196\text{cm}^2$ . Find the length of one side.

Possible Answers:

$14\text{cm}$

$13\text{cm}$

$15\text{cm}$

$18\text{cm}$

$16\text{cm}$

Correct answer:

$14\text{cm}$

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 $196\text{cm}^2$ . So, we will substitute and solve for b. So,

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

$\sqrt{196\text{cm}^2} = \sqrt{b^2}$

$14\text{cm} = b$

$b = 14\text{cm}$

Therefore, the length of one side of the square is 14cm.

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Example Question #354 : Geometry And Graphs

What of the following is NOT a property of a quadrilateral?

Possible Answers:

$\textup{All of the following are properties of a quadrilateral.}$

$\textup{The quadrilateral must contain at least a set of parallel edges.}$

$\textup{A quadrilateral must contain 4 edges and 4 vertices.}$

$\textup{The quadrilateral can be irregular.}$

$\textup{The interior angles must add up to 360 degrees.}$

Correct answer:

$\textup{The quadrilateral must contain at least a set of parallel edges.}$

Explanation:

A quadrilateral is a shape with four corners, or vertices, whose interior angles angles must sum up to 360 degrees.

The shape also has 4 edges.

The quadrilateral does not necessarily require two pairs of parallel lines.

Quadrilaterals may also be irregular.

The answer is:

$\textup{The quadrilateral must contain at least a set of parallel edges.}$

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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 #341 : 2 Dimensional Geometry

Example Question #342 : 2 Dimensional Geometry

Example Question #343 : Geometry And Graphs

Example Question #344 : Geometry And Graphs

Example Question #345 : Geometry And Graphs

Example Question #346 : Geometry And Graphs

Example Question #351 : Geometry And Graphs

Example Question #352 : Geometry And Graphs

Example Question #353 : Geometry And Graphs

Example Question #354 : Geometry And Graphs

All GED Math Resources

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