Answer:
7 square units
Step-by-step explanation:
As with many geometry problems, there are several ways you can work this.
Label the lower left and lower right vertices of the rectangle points W and E, respectively. You can subtract the areas of triangles WSR and EQR from the area of trapezoid WSQE to find the area of triangle QRS.
The applicable formulas are ...
area of a trapezoid: A = (1/2)(b1 +b2)h
area of a triangle: A = (1/2)bh
So, our areas are ...
AQRS = AWSQE - AWSR - AEQR
= (1/2)(WS +EQ)WE -(1/2)(WS)(WR) -(1/2)(EQ)(ER)
Factoring out 1/2, we have ...
= (1/2)((2+5)·4 -2·2 -5·2)
= (1/2)(28 -4 -10) = 7 . . . . square units
