Final answer:
To calculate the area of kite RSTU, split the kite into two congruent triangles RSU and RTU along the line RT and find the area of one triangle using the formula for a triangle's area, then double it. The area of kite RSTU is found to be 143 square units.
Step-by-step explanation:
To find the area of kite RSTU with vertices at R(0, 8), S(-4, -5), T(-8, -8), and U(-8, -3), we can split the kite into two triangles and find the areas of these triangles separately since the coordinates suggest that the kite is symmetrical about the line RT. The line RT splits the kite into two triangles RSU and RTU.
The area of a triangle can be calculated with the formula Area = 0.5 × base × height.
In triangle RSU, RS or RU can be considered as the base, and the height can be measured perpendicularly from T. Using the coordinates given, we can calculate these distances: |RS| = |RU| = sqrt((8+5)^2 + 4^2) = sqrt(169) = 13 units and the height (distance from T to line SU) = 8 + 3 = 11 units.
Thus, the area of triangle RSU is 0.5 × 13 × 11 = 71.5 square units.
Since RTU is a congruent triangle, it has the same area.
Therefore, the total area of kite RSTU is twice the area of triangle RSU, which is 2 × 71.5 = 143 square units.