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Advanced Geometry : Plane Geometry

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

Example Question #21 : How To Find The Length Of The Diagonal Of A Kite

If the area of the kite is 100 square units, and the difference between the lengths of the diagonals is units, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+10 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$100=\frac{x(x+10)}{2}$

x^2+10x=200

x^2+10x-200=0

(x+20)(x-10)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=10 .

The length of the shorter diagonal is units long.

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Example Question #22 : How To Find The Length Of The Diagonal Of A Kite

If the area a kite is square units, and the length of one diagonal is units longer than the other, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+5 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$88=\frac{x(x+5)}{2}$

x^2+5x=176

x^2+5x-176=0

(x+16)(x-11)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=11 .

The length of the shorter diagonal is units long.

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Example Question #23 : How To Find The Length Of The Diagonal Of A Kite

If the area of a kite is square units, and the length of one diagonal is units longer than the other, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+8 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$64=\frac{x(x+8)}{2}$

x^2+8x=128

x^2+8x-128=0

(x+16)(x-8)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=8 .

The length of the shorter diagonal is units long.

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Example Question #24 : How To Find The Length Of The Diagonal Of A Kite

If the area of a kite is 114 square units, and one diagonal is units longer than the other, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+7 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$114=\frac{x(x+7)}{2}$

x^2+7x=228

x^2+7x-228=0

(x+19)(x-12)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=12 .

The length of the shorter diagonal is units long.

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Example Question #25 : How To Find The Length Of The Diagonal Of A Kite

If the area of a kite is 104 square units, and the length of one diagonal is less than the other, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+3 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$104=\frac{x(x+3)}{2}$

x^2+3x=208

x^2+3x-208=0

(x+16)(x-13)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=13 .

The length of the shorter diagonal is units long.

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Example Question #26 : How To Find The Length Of The Diagonal Of A Kite

If the area of a kite is square units, and the length of one diagonal is units longer than the other, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+5 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$18=\frac{x(x+5)}{2}$

x^2+5x=36

x^2+5x-36=0

(x+9)(x-4)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=4 .

The length of the shorter diagonal is units long.

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Example Question #27 : How To Find The Length Of The Diagonal Of A Kite

If the area of a kite is square units, and one diagonal is units longer than the other, what is the length of the longer diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+3 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$20=\frac{x(x+3)}{2}$

x^2+3x=40

x^2+3x-40=0

(x+8)(x-5)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=5 .

To find the longer diagonal, add .

The length of the longer diagonal is units long.

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Example Question #28 : How To Find The Length Of The Diagonal Of A Kite

If the area of a kite is 1680 square units, and the length of one diagonal is units shorter than the other, what is the length of the shorter diagonal?

Possible Answers:

Correct answer:

Explanation:

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by x+4 .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$1680=\frac{x(x+4)}{2}$

x^2+4x=3360

x^2+4x-3360=0

(x+60)(x-56)=0

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, x=56 .

The length of the shorter diagonal is units long.

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Example Question #1 : Geometry

Which of the following shapes is a kite?

Shapes

Possible Answers:

A, B

Correct answer:

A, B

Explanation:

A kite is a four-sided shape with straight sides that has two pairs of sides. Each pair of adjacent sides are equal in length. A square is also considered a kite.

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Example Question #1 : How To Find The Area Of A Kite

What is the area of the following kite?

Kites

Possible Answers:

15m^2

10m^2

30m^2

8m^2

20m^2

Correct answer:

10m^2

Explanation:

The formula for the area of a kite:

$A = \frac{1}{2} (a)(b)$ ,

where represents the length of one diagonal and represents the length of the other diagonal.

Plugging in our values, we get:

$A = \frac{1}{2} (4\: m)(5\: m)$

$A = \frac{1}{2} (20\: m^2) = 10\: m^2$

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All Advanced Geometry Resources

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Advanced Geometry : Plane Geometry

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #21 : How To Find The Length Of The Diagonal Of A Kite

Example Question #22 : How To Find The Length Of The Diagonal Of A Kite

Example Question #23 : How To Find The Length Of The Diagonal Of A Kite

Example Question #24 : How To Find The Length Of The Diagonal Of A Kite

Example Question #25 : How To Find The Length Of The Diagonal Of A Kite

Example Question #26 : How To Find The Length Of The Diagonal Of A Kite

Example Question #27 : How To Find The Length Of The Diagonal Of A Kite

Example Question #28 : How To Find The Length Of The Diagonal Of A Kite

Example Question #1 : Geometry

Example Question #1 : How To Find The Area Of A Kite

All Advanced Geometry Resources

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