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: 

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: 

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: 

To find the length of the diagonal, we need to use the Pythagorean Theorem. Therefore, we need to sketch the following triangle within trapezoid :

We know that the base of the triangle has length . By subtracting the top of the trapezoid from the bottom of the trapezoid, we get:

Dividing by two, we have the length of each additional side on the bottom of the trapezoid:

Adding these two values together, we get .

The formula for the length of diagonal  uses the Pythagoreon Theorem:

, where  is the point between  and  representing the base of the triangle.

Plugging in our values, we get:

All of the lengths with one mark have length 5, and all of the side lengths with two marks have length 4. With this knowledge, we can add side lengths together to find that one diagonal is the hypotenuse to this right triangle:

Using Pythagorean Theorem gives:

take the square root of each side

Similarly, the other diagonal can be found with this right triangle:

Once again using Pythagorean Theorem gives an answer of

To find the length of the diagonals, split the top side into 3 sections as shown below:

The two congruent sections plus 8 adds to 14. , so the two congruent sections add to 6. They must each be 3. This means that the top of the right triangle with the diagonal as a hypotenuse must be 11, since .

We can solve for the diagonal, now pictured, using Pythagorean Theorem:

take the square root of both sides

To solve for the area of the rhombus , we must use the equation , where  and  are the diagonals of the rhombus. Since the perimeter of the rhombus is , and by definition all 4 sides of a rhombus have the same length, we know that the length of each side is . We can find the length of the other diagonal if we recognize that the two diagonals combined with a side edge form a right triangle. The length of the hypotenuse is , and each leg of the triangle is equal to one-half of each diagonal. We can therefore set up an equation involving Pythagorean's Theorem as follows:

, where  is equal to one-half the length of the unknown diagonal.

We can therefore solve for  as follows:

 is therefore equal to 8, and our other diagonal is 16. We can now use both diagonals to solve for the area of the rhombus:

The area of rhombus  is therefore equal to 

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of diagonal . From the problem, we are given that the sides are  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of diagonal . From the problem, we are given that the sides are  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of side . From the problem, we are given  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,