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Intermediate Geometry : How to find the area of a parallelogram

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Example Question #31 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is . Find the length of the base.

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+1)=6

Expand this equation.

x^2+x=6

x^2+x-6=0

Now factor this equation.

(x-2)(x+3)=6

Solve for .

x=2, x=-3

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Example Question #32 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is 100 . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x-48)=100

Expand this equation.

x^2-48x=100

x^2-48x-100=0

Now factor this equation.

(x-50)(x+2)=0

Solve for .

x=50, x=-2

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Example Question #31 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is 120 . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x-14)=120

Expand this equation.

x^2-14x=120

x^2-14x-120=0

Now factor this equation.

(x-20)(x+6)=0

Solve for .

x=20, x=-6

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Example Question #34 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is 240 . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+34)=240

Expand this equation.

x^2+34x=240

x^2+34x-240=0

Now factor this equation.

(x-6)(x+40)=0

Solve for .

x=6, x=-40

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Example Question #71 : Parallelograms

In the figure, the area of the parallelogram is . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+11)=80

Expand this equation.

x^2+11x=80

x^2+11x-80=0

Now factor this equation.

(x-5)(x+16)=0

Solve for .

x=5, x=-16

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Example Question #71 : Parallelograms

In the figure, the area of the parallelogram is . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+13)=90

Expand this equation.

x^2+13x=90

x^2+13x-90=0

Now factor this equation.

(x-5)(x+18)=0

Solve for .

x=5, x=-18

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Example Question #411 : Plane Geometry

In the figure, the area of the parallelogram is . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x-5)=84

Expand this equation.

x^2-5x=84

x^2-5x-84=0

Now factor this equation.

(x-12)(x+7)=0

Solve for .

x=12, x=-7

Since lengths of bases and heights can only be positive, x=12 .

Notice that the length of the base is given by the expression x-5 . Substitute in the value of to find the length of the base.

$\text{Length of Base}=x-5$

$\text{Length of Base}=12-5$

$\text{Length of Base}=7$

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Example Question #38 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is 150 . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+5)=150

Expand this equation.

x^2+5x=150

x^2+5x-150=0

Now factor this equation.

(x-10)(x+15)=0

Solve for .

x=10, x=-5

Since lengths of bases and heights can only be positive, x=10 .

Notice that the length of the base is given by the expression x+5 . Substitute in the value of to find the length of the base.

$\text{Length of Base}=x+5$

$\text{Length of Base}=10+5$

$\text{Length of Base}=15$

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Example Question #39 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is 500 . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+5)=500

Expand this equation.

x^2+5x=500

x^2+5x-500=0

Now factor this equation.

(x-20)(x+25)=0

Solve for .

x=20, x=-25

Since lengths of bases and heights can only be positive, x=20 .

Notice that the length of the base is given by the expression x+5 . Substitute in the value of to find the length of the base.

$\text{Length of Base}=x+5$

$\text{Length of Base}=20+5$

$\text{Length of Base}=25$

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Example Question #40 : How To Find The Area Of A Parallelogram

In the figure, the area of the parallelogram is 164 . Find the length of the base.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

x(x+37)=164

Expand this equation.

x^2+37x=164

x^2+37x-164=0

Now factor this equation.

(x-4)(x+41)=0

Solve for .

x=4, x=-41

Since lengths of bases and heights can only be positive, x=4 .

Notice that the length of the base is given by the expression x+37 . Substitute in the value of to find the length of the base.

$\text{Length of Base}=x+37$

$\text{Length of Base}=4+37$

$\text{Length of Base}=41$

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Intermediate Geometry : How to find the area of a parallelogram

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #31 : How To Find The Area Of A Parallelogram

Example Question #32 : How To Find The Area Of A Parallelogram

Example Question #31 : How To Find The Area Of A Parallelogram

Example Question #34 : How To Find The Area Of A Parallelogram

Example Question #71 : Parallelograms

Example Question #71 : Parallelograms

Example Question #411 : Plane Geometry

Example Question #38 : How To Find The Area Of A Parallelogram

Example Question #39 : How To Find The Area Of A Parallelogram

Example Question #40 : How To Find The Area Of A Parallelogram

All Intermediate Geometry Resources

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