Answer:
The are of QRSTU is 65 square units
B is correct.
Step-by-step explanation:
Please see the attachment for figure QRSTU
Q is at (3,0)
R is at (-3,0)
S is at (-3,7)
T is at (1,11)
U is at (5,7)
First we make three triangle. Join SQ and QT
We get three triangle
ΔSRQ, ΔSQT and ΔTQU
Area of triangle formula
[tex]\text{Area of triangle}=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
[tex]\text{Area of triangle SRQ}=\frac{1}{2}|-3(0-0)-3(0-7)+3(7-0)|=21\text{ square unit}[/tex]
[tex]\text{Area of triangle SQT}=\frac{1}{2}|-3(0-11)+3(11-7)+1(7-0)|=26\text{ square unit}[/tex]
[tex]\text{Area of triangle TQU}=\frac{1}{2}|1(0-7)-3(11-7)+5(0-11)|=18\text{ square unit}[/tex]
Area of QRSTU = ar(ΔSRQ) + ar(ΔSQT) + ar(ΔTQU)
Area of QRSTU = 21 + 26 + 18
= 65 square unit
Hence, The are of QRSTU is 65 square units
