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ACT Math : Kites

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Example Questions

Example Question #51 : Kites

A kite has a side length of $15\textup{ inches}$ and another side length of $30\textup{ inches}$ . Find the perimeter of the kite.

Possible Answers:

$45\textup{ inches}$

$7.5\textup{ feet}$

$87\textup{ inches}$

$90 \textup{ cm}$

$12\textup{ feet}$

Correct answer:

$7.5\textup{ feet}$

Explanation:

By definition a kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side with a length of , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(15+30)

$p=2(45)=90\textup{ inches}$

Note, though, that $90\textup{ inches}$ does not appear as an answer choice. Thus, convert $90\textup{ inches}$ into $\textup{feet}$ by: $90\div12=7.5\textup{ feet}$

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Example Question #51 : Quadrilaterals

A kite has a side length of $88\textup{mm}$ and another side length of $36\textup{mm}$ . Find the perimeter of the kite.

Possible Answers:

$209\textup{cm}$

$264\textup{mm}$

$176\textup{mm}$

$248\textup{mm}$

$209\textup{mm}$

Correct answer:

$248\textup{mm}$

Explanation:

a kite must have two sets of equivalent sides. Since we know that this kite has a side length of $88\textup{mm}$ and another side with a length of $36\textup{mm}$ , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(88+36)

$p=2(124)=248\textup{mm}$

Note: the correct solution can also be found by:

p=88+88+36+36=176+72=248

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Example Question #52 : Quadrilaterals

A kite has a side length of $12\textup{cm}$ and another side length of $16\textup{cm}$ . Find the perimeter of the kite.

Possible Answers:

$24\textup{cm}$

$96\textup{in}$

$60\textup{cm}$

$56\textup{cm}$

$90\textup{cm}$

Correct answer:

$56\textup{cm}$

Explanation:

A kite must have two sets of equivalent sides. Since we know that this kite has a side length of and another side length of , each of these two sides must have one equivalent side.

The perimeter of this kite can be found by applying the formula:

p=2(a+b)

p=2(12+16)

$p=2(28)=56\textup{cm}$

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Example Question #51 : Quadrilaterals

Find the area of a kite with the diagonal lengths of and .

Possible Answers:

2ab

4a+4b

2a+2b

4ab

Correct answer:

2ab

Explanation:

Write the formula to find the area of a kite. Substitute the diagonals and solve.

$A=\frac{d1 \cdot d2}{2} = \frac{2a \cdot 2b}{2} =2ab$

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

Find the area of a kite with diagonal lengths of a+b and 2a-2b .

Possible Answers:

2a^2+2b^2

a^2+b^2

a^2-ab-b^2

a^2-b^2

2a^2-2b^2

Correct answer:

a^2-b^2

Explanation:

Write the formula for the area of a kite.

$A= \frac{d1\cdot d2}{2}$

Plug in the given diagonals.

$A= \frac{(a+b)\cdot (2a-2b)}{2}$

Pull out a common factor of two in 2a-2b and simplify.

$A= \frac{(a+b)\cdot2(a-b)}{2}$

A=(a+b)(a-b)

Use the FOIL method to simplify.

A=(a+b)(a-b)= (a)(a)+(a)(-b)+(b)(a)+(b)(-b)

A= a^2-b^2

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

Find the area of a kite if one diagonal is $2\:cm$ long, and the other diagonal is $10\:cm$ long.

Possible Answers:

$10\sqrt3\:cm^2$

$20\:cm^2$

$10\:cm^2$

$3\sqrt{10}$ cm^2

$10\sqrt2\:cm^2$

Correct answer:

$10\:cm^2$

Explanation:

The formula for the area of a kite is

$A=\frac{d_1\cdot d_2}{2}$

Plug in the values for each of the diagonals and solve.

$A = \frac{2\cdot 10}{2}=\frac{20}{2}=10\:cm^2$

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ACT Math : Kites

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #51 : Kites

Example Question #51 : Quadrilaterals

Example Question #52 : Quadrilaterals

Example Question #51 : Quadrilaterals

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

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

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