Question

A rectangle is drawn on a coordinate plane with vertices (0,0), (2,2), (9,−4), and (7,−6). Using the coordinates, what is the approximate area of the rectangle? (1 point)
Responses

52.2 units2
52.2 u n i t s squared

24.1 units2
24.1 u n i t s squared

12.05 units2
12.05 u n i t s squared

26.08 units2
26.08 u n i t s squared

Answer 1

Use the shoelace formula with the points in order (0,0), (2,2), (9,−4), (7,−6):

Sum1 = 0·2 + 2·(−4) + 9·(−6) + 7·0 = −62
Sum2 = 0·2 + 2·9 + (−4)·7 + (−6)·0 = −10

Area = 1/2 |Sum1 − Sum2| = 1/2 |−62 − (−10)| = 1/2·52 = 26

So the area is 26 ≈ 26.08 units². Select 26.08 units².