Kite TQRS's points are T(0,0), Q(0,3), R(5,5), S(3,0). How do I find the area?

Question

Im having trouble finding the length of the diagonals

Answer 1

Solution 1:

If the diagonals in a quadrilateral are perpendicular to each other then the area is one half or the product of the diagonals.

All Kites and rhombi fall in this category.

In your case the diagonals are TR and QS so. By the distance formula,

|TR| = √[(5-0)²+(5-0)²] = √50 = 5√2 and

|QS| = √[(3-0)²+(0-3)²] = √18 = 3√2

so Area(TQRS) = |TR|*|QS|/2=5√2*3√2 / 2 = 15

Solution 2 (Pick's Theorem):

For simple polygons, whose vertices all have integer coordinates (lattice points), if I is the number of lattice points interior to the polygon and B is the number of lattice points on the perimeter then the polygon's area is B/2+I-1.

In polygon TQRS we have B=8 and I=12 so the Area(TQRS) = 8/2+12-1 = 15

Answer 2

A kite's area = (1/2) of the product of the two diagonals.

TR = 5sqrt(2), diagonal 1

QS = 3sqrt(2), diagonal 2

So, the area = 15