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Advanced Geometry : Advanced Geometry

Study concepts, example questions & explanations for Advanced Geometry

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6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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 #321 : Advanced Geometry

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 : How To Find The Area Of A Kite

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 #11 : Geometry

What is the area of the following kite?

Kites

Possible Answers:

15m^2

10m^2

8m^2

30m^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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Example Question #1 : How To Find The Area Of A Kite

Two congruent equilateral triangles with sides of length are connected so that they share a side. Each triangle has a height of . Express the area of the shape in terms of .

Possible Answers:

h^2

$\frac{h}{2}$

Correct answer:

Explanation:

The shape being described is a rhombus with side lengths 1. Since they are equilateral triangles connected by one side, that side becomes the lesser diagonal, so p=1 .

The greater diagonal is twice the height of the equaliteral triangles, q=2h .

The area of a rhombus is half the product of the diagonals, so:

$A=\frac{pq}{2}=\frac{1 \cdot 2h}{2}=h$

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Example Question #2 : How To Find The Area Of A Kite

Find the area of a kite if the diagonal dimensions are x+3 and x-6 .

Possible Answers:

$(x^2-3x-18)\sqrt2$

$\frac{x^2-3x+18}{2}$

x^2+3x-18

$\frac{x^2-3x-18}{2}$

$\frac{x^2+3x-18}{2}$

Correct answer:

$\frac{x^2-3x-18}{2}$

Explanation:

The area of the kite is given below. The FOIL method will need to be used to simplify the binomial.

$A=\frac{d1\cdot d2}{2}=\frac{(x+3)(x-6)}{2}= \frac{x^2-6x+3x-18}{2}$

$A= \frac{x^2-3x-18}{2}$

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All Advanced Geometry Resources

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Advanced Geometry : Advanced Geometry

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

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

Example Question #321 : Advanced Geometry

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 : How To Find The Area Of A Kite

Example Question #11 : Geometry

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

Example Question #2 : How To Find The Area Of A Kite

All Advanced Geometry Resources

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