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High School Math : How to find the area of a kite

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

What is the area of a kite with diagonals of 5 and 7?

Possible Answers:

$\displaystyle 24$

$\displaystyle 35$

17.5 $\displaystyle 17.5$

$\displaystyle 25$

Correct answer:

17.5 $\displaystyle 17.5$

Explanation:

To find the area of a kite using diagonals you use the following equation $\frac{a*b}{2}=Area\: of a\: kite$ $\displaystyle \frac{a*b}{2}=Area\: of a\: kite$

That diagonals ($\displaystyle a$ and $\displaystyle b$)are the lines created by connecting the two sides opposite of each other.

Plug in the diagonals for $\displaystyle a$ and $\displaystyle b$ to get $\frac{5*7}{2}=Area$ $\displaystyle \frac{5*7}{2}=Area$

Then multiply and divide to get the area. $\frac{35}{2}=17.5$ $\displaystyle \frac{35}{2}=17.5$

The answer is 17.5 $\displaystyle 17.5$

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Example Question #1 : Quadrilaterals

Find the area of the following kite:

Kite

Possible Answers:

26m^2 $\displaystyle 26m^2$

39m^2 $\displaystyle 39m^2$

78m^2 $\displaystyle 78m^2$

54m^2 $\displaystyle 54m^2$

27m^2 $\displaystyle 27m^2$

Correct answer:

39m^2 $\displaystyle 39m^2$

Explanation:

The formula for the area of a kite is:

$A = \frac{1}{2}(d_{1}\cdot d_{2})$ $\displaystyle A = \frac{1}{2}(d_{1}\cdot d_{2})$

Where $d_{1}$ $\displaystyle d_{1}$ is the length of one diagonal and $d_{2}$ $\displaystyle d_{2}$ is the length of the other diagonal

Plugging in our values, we get:

$A = \frac{1}{2}(d_{1}\cdot d_{2})$ $\displaystyle A = \frac{1}{2}(d_{1}\cdot d_{2})$

$A = \frac{1}{2}(6m\cdot 13m) = 39m^2$ $\displaystyle A = \frac{1}{2}(6m\cdot 13m) = 39m^2$

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

Find the area of the following kite:

Screen_shot_2014-03-01_at_9.16.34_pm

Possible Answers:

$18\sqrt{3}m^2$ $\displaystyle 18\sqrt{3}m^2$

$18\sqrt{3}-18m^2$ $\displaystyle 18\sqrt{3}-18m^2$

$18\sqrt{3}+18m^2$ $\displaystyle 18\sqrt{3}+18m^2$

18m^2 $\displaystyle 18m^2$

20m^2 $\displaystyle 20m^2$

Correct answer:

$18\sqrt{3}+18m^2$ $\displaystyle 18\sqrt{3}+18m^2$

Explanation:

The formula for the area of a kite is:

$A = \frac{1}{2} (d_1)(d_2)$ $\displaystyle A = \frac{1}{2} (d_1)(d_2)$

where d_1 $\displaystyle d_1$ is the length of one diagonal and d_2 $\displaystyle d_2$ is the length of another diagonal.

Use the formulas for a $\displaystyle 45-45-90$ triangle and a $\displaystyle 30-60-90$ triangle to find the lengths of the diagonals. The formula for a $\displaystyle 45-45-90$ triangle is $a-a-a \sqrt{2}$ $\displaystyle a-a-a \sqrt{2}$ and the formula for a $\displaystyle 30-60-90$ triangle is $a-a \sqrt{3}-2a$ $\displaystyle a-a \sqrt{3}-2a$.

Our $\displaystyle 45-45-90$ triangle is: $3 \sqrt{2}m-3 \sqrt{2}m-6m$ $\displaystyle 3 \sqrt{2}m-3 \sqrt{2}m-6m$

Our $\displaystyle 30-60-90$ triangle is: $3 \sqrt{2}m-3 \sqrt{6}m-6\sqrt{2}m$ $\displaystyle 3 \sqrt{2}m-3 \sqrt{6}m-6\sqrt{2}m$

Plugging in our values, we get:

$A = \frac{1}{2} (d_1)(d_2)$ $\displaystyle A = \frac{1}{2} (d_1)(d_2)$

$A = \frac{1}{2} (6\sqrt{2}m) (3\sqrt{6}m + 3\sqrt{2}m)$ $\displaystyle A = \frac{1}{2} (6\sqrt{2}m) (3\sqrt{6}m + 3\sqrt{2}m)$

$A = \frac{1}{2} (18\sqrt{12}+18\sqrt{4}) = 18\sqrt{3}+18m^2$ $\displaystyle A = \frac{1}{2} (18\sqrt{12}+18\sqrt{4}) = 18\sqrt{3}+18m^2$

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High School Math : How to find the area of a kite

Study concepts, example questions & explanations for High School Math

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Example Questions

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

Example Question #1 : Quadrilaterals

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

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