The area of the trapezium is 51 square units.
According to the coordinates given, we can assume that the vertices are listed in the following order:
- S(-4, 8)
- *P(-7, 2)
- Q(3, 2)
- R(3, 8)
This implies that SR and *PQ are the parallel sides, and we'll calculate the distance between them to find the height of the trapezium. Here's how you can calculate the area step-by-step:
Step 1: Calculate the length of the top base (SR). Since both points have the same y-coordinate (y = 8), we can simply find the distance by calculating the difference between their x-coordinates.
SR = R_x - S_x
= 3 - (-4)
= 3 + 4
= 7 units
Step 2: Calculate the length of the bottom base (*PQ). Similarly, both points have the same y-coordinate (y = 2), so we again calculate the difference between their x-coordinates.
*PQ = Q_x - P*_x
= 3 - (-7)
= 3 + 7
= 10 units
Step 3: Find the height (h) of the trapezium. The height is the distance between the y-coordinates of the parallel sides. We can take the y-coordinates of S and *P for this, as S and R have the same y-coordinate, as do *P and Q.
h = S_y - P*_y
= 8 - 2
= 6 units
Step 4: Finally, we can use the area formula for a trapezium:
Area = 0.5 × (Sum of parallel sides) × Height
= 0.5 × (SR + *PQ) × h
= 0.5 × (7 + 10) × 6
= 0.5 × 17 × 6
= 8.5 × 6
= 51 square units
So the area of the trapezium is 51 square units.