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ACT Math : Quadrilaterals

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Example Question #9 : How To Find The Length Of The Diagonal Of A Kite

Kite vt act

The area of the kite shown above is $125\textup{ units}^{2}$ and the red diagonal has a length of . Find the length of the black (horizontal) diagonal.

Possible Answers:

Correct answer:

Explanation:

To find the length of the black diagonal apply the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$125=\frac{25\times diagonal B}{2}$

$125\times2=25\times diagonalB$

250=25(diagonalB)

$diagonal B=\frac{250}{25}=10$

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Example Question #2 : Kites

A kite has two perpendicular interior diagonals. One diagonal has a measurement of $22\textup{mm}$ and the area of the kite is $297\textup{mm}^{2}$ . Find the length of the other interior diagonal.

Possible Answers:

$25\textup{mm}$

$37\textup{mm}$

$35\textup{mm}$

$27\textup{mm}$

$19\textup{mm}$

Correct answer:

$27\textup{mm}$

Explanation:

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$297=\frac{22\times diagonal B}{2}$

$297\times2=22\times diagonalB$

594=22(diagonalB)

$diagonal B=\frac{594}{22}=27$

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

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $54\textup{ units}^{2}$ . Find the length of the other interior diagonal.

Possible Answers:

Correct answer:

Explanation:

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$54=\frac{9\times diagonal B}{2}$

$54\times2=9\times diagonalB$

108=9(diagonalB)

$diagonal B=\frac{108}{9}=12$

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Example Question #11 : Quadrilaterals

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $1\textup{,}800\textup{ units}^{2}$ . Find the sum of the two perpendicular interior diagonals.

Possible Answers:

$3\textup{,}000$

130

Correct answer:

130

Explanation:

You must find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals.

To find the missing diagonal, apply the area formula:

This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

$1800=\frac{40\times diagonal B}{2}$

$1800\times2=40\times diagonalB$

3,600=40(diagonalB)

$diagonal B=\frac{3,600}{40}=90$

Therefore, the sum of the two diagonals is:

90+40=130

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Example Question #11 : How To Find The Length Of The Diagonal Of A Kite

A kite has two perpendicular interior diagonals. One diagonal has a measurement of and the area of the kite is $51\textup{ units}^{2}$ . Find the sum of the two perpendicular interior diagonals.

Possible Answers:

Correct answer:

Explanation:

First find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals.

To find the missing diagonal, apply the area formula:

This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

$51=\frac{17\times diagonal B}{2}$

$51\times2=17\times diagonalB$

102=17(diagonalB)

$diagonal B=\frac{102}{17}=6$

Therefore, the sum of the two diagonals is:

17+6=23

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Example Question #11 : How To Find The Length Of The Diagonal Of A Kite

A kite has two perpendicular interior diagonals. One diagonal has a measurement of $38\textup{cm}$ and the area of the kite is $855\textup{cm}^{2}$ . Find the length of the other interior diagonal.

Possible Answers:

$48\textup{cm}$

$22.5\textup{cm}$

$45\textup{cm}$

$33\textup{cm}$

$15\textup{cm}$

Correct answer:

$45\textup{cm}$

Explanation:

This problem can be solved by applying the area formula:

Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal.

Thus the solution is:

$855=\frac{38\times diagonal B}{2}$

$855\times2=38\times diagonalB$

1,710=38(diagonalB)

$diagonal B=\frac{1,710}{38}=45$

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Example Question #21 : Kites

The long diagonal of a kite measures inches, and cuts the shorter diagonal into two pieces. If one of those pieces measures inches, what is the length in inches of the short diagonal?

Possible Answers:

6in

11in

10in

8in

Correct answer:

8in

Explanation:

The long diagonal of a kite always bisects the short diagonal. Therefore, if one side of the bisected diagonal is inches, the entire diagonal is inches. It does not matter how long the long diagonal is.

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

A kite has two adjacent sides both with a measurement of . The perimeter of the kite is . Find the length of one of the remaining two sides.

Possible Answers:

$\frac{8}{3}$

Correct answer:

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

30=8+8+2(side) , where side= one of the two missing sides.

30=16+2(sides)

2(sides)=30-16 = 14

$side=\frac{14}{2}=7$

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

A kite has two adjacent sides both with a measurement of . The perimeter of the kite is 300 . Find the length of one of the remaining two sides.

Possible Answers:

184

116

Correct answer:

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided. Then divide that remaining difference in half, because each of the two sides must have the same length.

The solution is:

300=92+92+2(side) , where side= one of the two missing sides.

300=184+2(sides)

2(sides)=300-184 = 116

$side=\frac{116}{2}=58$

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Example Question #3 : How To Find The Length Of The Side Of A Kite

Kite vt act

Using the kite shown above, find the length of side .

Possible Answers:

137

213

113

226

103

Correct answer:

113

Explanation:

A kite must have two sets of congruent adjacent sides. This question provides the length for one set of congruent adjacent sides, thus the two remaining sides must be congruent to each other. Since, this problem also provides the perimeter measurement of the kite, find the difference between the perimeter and the sum of the congruent adjacent sides provided.

The solution is:

500=137+137+2(side) , where side= one of the two missing sides.

500=274+2(sides)

2(sides)=500-274 = 226
Since the remaining two sides have a total length of 226 , side must be $\frac{226}{2}=113$

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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #9 : How To Find The Length Of The Diagonal Of A Kite

Example Question #2 : Kites

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

Example Question #11 : Quadrilaterals

Example Question #11 : How To Find The Length Of The Diagonal Of A Kite

Example Question #11 : How To Find The Length Of The Diagonal Of A Kite

Example Question #21 : Kites

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

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

Example Question #3 : How To Find The Length Of The Side Of A Kite

All ACT Math Resources

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