We know that kites have two pairs of congruent sides. If one side is 7 m long, then we have another side of the same length. The remaining 6 m of perimeter is split up evenly too, so we have two sides of length 7 m and two sides of length 3 m. We know that the shorter diagonal is 4 m long, which means we can find the length of the other diagonal using the Pythagorean theorem for each portion of the unknown diagonal. The first triangle has a leg of 2 m and a hypotenuse of 3 m. a^{2} + b^{2} = c^{2} 2^{2} + b^{2} = 3^{2} b^{2} = 5
The other has a leg of 2 m and a hypotenuse of 7 m. a^{2} + b^{2} = c^{2} 2^{2} + b^{2} = 7^{2} b^{2} = 45
If we combine them, we can see that the unknown diagonal has a length of . Calculating the area shouldn't be a problem now.
A = 17.9 m^{2}
