Answer: The area of triangle QUV is 24 square feet
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Explanation:
Segment TV is the base of the green parallelogram PRTV The height is segment RS which is 8 ft. This is marked as the perpendicular dashed segment line (note the right angle marker). RS is perpendicular to SV, which in turn means RS is perpendicular to TV as well.
Area of Parallelogram = Base*Height 96 = TV*RS 96 = TV*8 96/8 = TV 12 = TV TV = 12
Segment TV is composed of TU and UV, both of which are congruent segments. The single tickmarks show this. The instructions also state "the lengths of segment TU an segment UV are equal" So TU = UV TU + UV = TV UV + UV = TV 2*UV = TV 2*UV = 12 UV = 12/2 UV = 6
The height of triangle QUV is also RS = 8 because triangle QUV is completely enclosed inside the parallelogram, and because RS is perpendicular to UV. The base of triangle QUV is the segment UV = 6
Area of triangle QUV = (base)*(height)/2 Area of triangle QUV = UV*RS/2 Area of triangle QUV = 6*8/2 Area of triangle QUV = 48/2 Area of triangle QUV = 24 square feet
