GED Math : 2-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #21 : Area Of A Quadrilateral

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

Possible Answers:

\displaystyle 8x^2+4x+1

\displaystyle 8x+1

\displaystyle 16x^2+8x+1

\displaystyle 16x^2+1

\displaystyle 8x+4

Correct answer:

\displaystyle 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.

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

The area of a square is:  \displaystyle s^2

Square the quantity of the side.

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

Use the FOIL method to solve.

\displaystyle (4x)(4x)+(4x)(1)+ (1)(4x)+(1)(1)

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

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

Example Question #22 : Area Of A Quadrilateral

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

Possible Answers:

\displaystyle 121\text{in}^2

\displaystyle 144\text{in}^2

\displaystyle 111\text{in}^2

\displaystyle 110\text{in}^2

\displaystyle 132\text{in}^2

Correct answer:

\displaystyle 121\text{in}^2

Explanation:

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

\displaystyle 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

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

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

Example Question #23 : Area Of A Quadrilateral

Use the following rectangle to answer the question:

Rectangle4

Find the area.

Possible Answers:

\displaystyle 16\text{cm}^2

\displaystyle 54\text{cm}^2

\displaystyle 32\text{cm}^2

\displaystyle 63\text{cm}^2

\displaystyle 72\text{cm}^2

Correct answer:

\displaystyle 63\text{cm}^2

Explanation:

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

\displaystyle 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

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

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

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:

\displaystyle 72\text{in}^2

\displaystyle 18\text{in}^2

\displaystyle 36\text{in}^2

\displaystyle 96\text{in}^2

\displaystyle 54\text{in}^2

Correct answer:

\displaystyle 72\text{in}^2

Explanation:

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

\displaystyle 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

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

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

Example Question #31 : Area Of A Quadrilateral

What is the area of a square with a perimeter of \displaystyle 3?

Possible Answers:

\displaystyle \frac{9}{16}

\displaystyle \frac{9}{8}

\displaystyle \frac{9}{2}

\displaystyle 9

\displaystyle \frac{9}{4}

Correct answer:

\displaystyle \frac{9}{16}

Explanation:

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

\displaystyle 4s=3

Divide by 4 on each side.

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

Each side has a length of three fourths.

Write the formula for the area of a square.

\displaystyle A=s^2

Substitute the side.

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

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

Example Question #32 : Area Of A Quadrilateral

Find the area of a rectangle with a length of \displaystyle 8x and a height of \displaystyle 4x^2.

Possible Answers:

\displaystyle 32 x^3

\displaystyle 32 x^2

\displaystyle 24x^3

\displaystyle 16x^3

\displaystyle 24x^2

Correct answer:

\displaystyle 32 x^3

Explanation:

Write the formula to find the area of a rectangle.

\displaystyle A = LW

Substitute the dimensions.

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

The answer is:  \displaystyle 32 x^3

Example Question #33 : Area Of A Quadrilateral

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

Possible Answers:

\displaystyle 45

\displaystyle 15

\displaystyle 25

\displaystyle 60

\displaystyle 30

Correct answer:

\displaystyle 45

Explanation:

Write the area formula for a square.

\displaystyle A = s^2

Substitute the side length in the equation.

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

The area is:  \displaystyle 45

Example Question #34 : Area Of A Quadrilateral

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

Possible Answers:

\displaystyle 5944.4

\displaystyle 77.1

\displaystyle 1486.1

\displaystyle 1322.4

Correct answer:

\displaystyle 1486.1

Explanation:

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

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

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

For the given square,

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

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

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

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

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

Example Question #35 : Area Of A Quadrilateral

Use the following rectangle to answer the question:

Rectangle4

Find the area.

Possible Answers:

\displaystyle 32\text{cm}^2

\displaystyle 63\text{cm}^2

\displaystyle 54\text{cm}^2

\displaystyle 16\text{cm}^2

\displaystyle 72\text{cm}^2

Correct answer:

\displaystyle 63\text{cm}^2

Explanation:

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

\displaystyle 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

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

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

Example Question #36 : Area Of A Quadrilateral

Use the following square to answer the question:

Square3

Find the area.

Possible Answers:

\displaystyle 64\text{cm}^2

\displaystyle 24\text{cm}^2

\displaystyle 56\text{cm}^2

\displaystyle 32\text{cm}^2

\displaystyle 16\text{cm}^2

Correct answer:

\displaystyle 64\text{cm}^2

Explanation:

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

\displaystyle 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

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

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

Learning Tools by Varsity Tutors