Calculate AO Length in Kite ABCD: Given Area 42 cm² and Diagonal 14 units

The kite ABCD shown below has an area of 42 cm².

AB = BC

DC = AD

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

S=42S=42S=42141414DDDAAABBBCCCOOO

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:16 Let's calculate the length of side AO.
00:19 We'll use the kite area formula.
00:22 It's diagonal one times diagonal two, divided by two.
00:28 Now, substitute the given values to find diagonal AC.
00:49 This gives us the length of diagonal AC.
00:55 Remember, the main diagonal intersects the secondary diagonal.
01:00 And that's how we solve this problem. Great job!

Step-by-step written solution

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1

Understand the problem

The kite ABCD shown below has an area of 42 cm².

AB = BC

DC = AD

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

S=42S=42S=42141414DDDAAABBBCCCOOO

2

Step-by-step solution

We substitute the data we have into the formula for the area of the kite:

S=AC×BD2 S=\frac{AC\times BD}{2}

42=AC×142 42=\frac{AC\times14}{2}

We multiply by 2 to remove the denominator:

14AC=84 14AC=84

Then divide by 14:

AC=6 AC=6

In a rhombus, the main diagonal crosses the second diagonal, therefore:

AO=AC2=62=3 AO=\frac{AC}{2}=\frac{6}{2}=3

3

Final Answer

3 cm

Practice Quiz

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The next quadrilateral is:

AAABBBCCCDDD

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