How do you find area of a kite when the diagonals are not given?

Answer 1

You do not need to know the length of the diagonals to find the area of a kite.

A kite is essentially four triangles combined, so you just find the area of the four individual triangles and add them together.

In actuality, the two triangles that make up the top of the kite form a mathematical rectangle, as do the two triangles that comprise the bottom, because the formula for finding the area of a triangle is simply taking one-half the area of the rectangle that would be formed by the legs of the triangle, and two times one-half equals one whole.

Let's look at a kite and the formula. For the sake of this example we'll say that a kite is composed of a vertical and a horizontal member, which intersect at some point. The horizontal member is bisected (intersected in the middle) While the vertical member can be intersected at any number of points depending on the design of the kite. Typically, the vertical member will be intersected closer to the top to achieve the classic kite configuration.

On our kite we will call the length of the vertical member above the intersection of the two kite sticks "a", the length of the vertical section below the intersection "b" and the length of the horizontal stick on either side of the intersection "c". Our formula for the area of the kite now becomes:

1/2(a X c) + 1/2(a X c) + 1/2(b X c) + 1/2(b X c)

Which in reality (simpler terms) is:

(a X c) + (b X c)

To plug in some numbers, let's take two kite sticks, the vertical stick being 4' long, the horizontal stick 2.5' long. The intersection of the sticks leaves 2.5' for the bottom section of the vertical and 1.5' for the upper section of the vertical. The horizontal stick is cut in half, or 1.25' on each side of the intersection. Our area then is:

(1.5 X 1.25) + (2.5 X 1.25) = 1.875 + 3.125 = 5 square feet.

As you can see, the length of the diagonals never entered into our equation.