So imagine a triangle whose base is the base of the rhombus, but whose apex is the **middle**, then use Pythagoras Theorem

a[sup]2[/sup] + b[sup]2[/sup] = c[sup]2[/sup]

Remember, these are going to be half-diagonals, so the difference will only be 2, and lets call the short diagonal "x":

x[sup]2[/sup] + (x+2)[sup]2[/sup] = 10[sup]2[/sup]

x[sup]2[/sup] + x[sup]2[/sup] + 4x + 2[sup]2[/sup] = 10[sup]2[/sup]

2x[sup]2[/sup] + 4x + 4 = 100

2x[sup]2[/sup] + 4x -96 = 0

This is a Quadratic Equation and the solutions are 6 and -8. The lengths won't be negative so "6" is the answer.

That is the short "half-diagonal", so the full diagonal will be 12, and the longer diagonal 16.

The area will be ½ × 12 × 16 = 96 (because you can calculate the area of a rhombus by multiplying the diagonals and then halving)

]]>picture of kite without the tail flying in the wind.

Notice the right triangles.

Assign values like x and x-2 and 10 and apply pythagoreans theorm

Then solve the quadratic equation using quadratic formula if it's hard.

Then the area is four right triangles, or two rectangles, if you pair up

the right triangles by sliding them all around.]]>

so all sides are 10. Hope that helps you.]]>