Kites
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ACT Math › Kites
A kite has two adjacent sides both with a measurement of 
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:
The long diagonal of a kite measures 
Explanation
The long diagonal of a kite always bisects the short diagonal. Therefore, if one side of the bisected diagonal is 
Find the area of a kite with diagonal lengths of 
Explanation
Write the formula for the area of a kite.
Plug in the given diagonals.
Pull out a common factor of two in 
Use the FOIL method to simplify.
The long diagonal of a kite measures
Explanation
The long diagonal of a kite always bisects the short diagonal. Therefore, if one side of the bisected diagonal is
A kite has two adjacent sides both with a measurement of
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:
A kite has a side length of 
Explanation
By definition a kite must have two sets of equivalent sides. Since we know that this kite has a side length of 
The perimeter of this kite can be found by applying the formula:
Note: the correct solution can also be found by:
The original formula used in this solution is an application of the Distributive Property:
A kite has a side length of
Explanation
By definition a kite must have two sets of equivalent sides. Since we know that this kite has a side length of
The perimeter of this kite can be found by applying the formula:
Note: the correct solution can also be found by:
The original formula used in this solution is an application of the Distributive Property:
Find the area of a kite with diagonal lengths of
Explanation
Write the formula for the area of a kite.
Plug in the given diagonals.
Pull out a common factor of two in
Use the FOIL method to simplify.
If the diagonals of the quadrilateral above were drawn in the figure, they would form four 90 degree angles at the center. In degrees, what is the value of 
Explanation
A quadrilateral is considered a kite when one of the following is true:
(1) it has two disjoint pairs of sides are equal in length or
(2) one diagonal is the perpendicular bisector of the other diagonal. Given the information in the question, we know (2) is definitely true.
To find 
The sum of angles within any quadrilateral is 360 degrees.
Therefore 
To find 
If the diagonals of the quadrilateral above were drawn in the figure, they would form four 90 degree angles at the center. In degrees, what is the value of
Explanation
A quadrilateral is considered a kite when one of the following is true:
(1) it has two disjoint pairs of sides are equal in length or
(2) one diagonal is the perpendicular bisector of the other diagonal. Given the information in the question, we know (2) is definitely true.
To find
The sum of angles within any quadrilateral is 360 degrees.
Therefore
To find