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Example Questions
Example Question #1 :How To Find The Length Of The Diagonal Of A Kite
The area of the rectangle is, what is the area of the kite?
The area of a kite is half the product of the diagonals.
The diagonals of the kite are the height and width of the rectangle it is superimposed in, and we know that because the area of a rectangle is base times height.
Therefore our equation becomes:
.
We also know the area of the rectangle is.Substituting this value in we get the following:
Thus,, the area of the kite is.
Example Question #10 :Calculating The Length Of The Diagonal Of A Quadrilateral
Given: Quadrilateralsuch that,,,is a right angle, and diagonalhas length 24.
Give the length of diagonal.
None of the other responses is correct.
The Quadrilateralis shown below with its diagonalsand.
.We call the point of intersection:
The diagonals of a quadrilateral with two pairs of adjacent congruent sides - akite- are perpendicular; also,bisects theandangles of the kite. Consequently,is a 30-60-90 triangle andis a 45-45-90 triangle. Also, the diagonal that connects the common vertices of the pairs of adjacent sides bisects the other diagonal, making的中点.Therefore,
.
By the 30-60-90 Theorem, sinceandare the short and long legs of,
By the 45-45-90 Theorem, sinceandare the legs of a 45-45-90 Theorem,
.
The diagonalhas length
.
Example Question #1 :How To Find The Length Of The Diagonal Of A Kite
Using the kite shown above, find the length of the red (vertical) diagonal.
In order to solve this problem, first observe that the red diagonal line divides the kite into two triangles that each have side lengths ofandNotice, the hypotenuse of the interior triangle is the red diagonal. Therefore, use the Pythagorean theorem:, wherethe length of the red diagonal.
The solution is:
Example Question #3 :How To Find The Length Of The Diagonal Of A Kite
A kite has two perpendicular interior diagonals. One diagonal is twice the length of the other diagonal. The total area of the kite is.找到每个室内对角线的长度。
To solve this problem, apply the formula for finding the area of a kite:
However, in this problem the question only provides information regarding the exact area. The lengths of the diagonals are represented as a ratio, where
Therefore, it is necessary to plug the provided information into the area formula. Diagonalis represented byand diagonal.
The solution is:
Thus, if, then diagonalmust equal
Example Question #4 :How To Find The Length Of The Diagonal Of A Kite
A kite has two perpendicular interior diagonals. One diagonal has a measurement ofand the area of the kite is.Find the length of the other interior diagonal.
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:
Example Question #5 :How To Find The Length Of The Diagonal Of A Kite
A kite has two perpendicular interior diagonals. One diagonal has a measurement ofand the area of the kite is.Find the length of the other interior diagonal.
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:
Example Question #6 :How To Find The Length Of The Diagonal Of A Kite
A kite has two perpendicular interior diagonals. One diagonal has a measurement ofand the area of the kite is.Find the sum of the two perpendicular interior diagonals.
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.
Therefore, the sum of the two diagonals is:
Example Question #7 :How To Find The Length Of The Diagonal Of A Kite
A kite has two perpendicular interior diagonals. One diagonal has a measurement ofand the area of the kite is.Find the sum of the two perpendicular interior diagonals.
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.
Therefore, the sum of the two diagonals is:
Example Question #8 :How To Find The Length Of The Diagonal Of A Kite
The area of the kite shown above isand the red diagonal has a length of.Find the length of the black (horizontal) diagonal.
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:
Example Question #9 :How To Find The Length Of The Diagonal Of A Kite
A kite has two perpendicular interior diagonals. One diagonal has a measurement ofand the area of the kite is.Find the length of the other interior diagonal.
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: