Answer: see below
Step-by-step explanation:
The shape is a trapezoid
Base 1 (BH) is 10
Base 2 (QA) is 14
Height is 5
Area
[tex]A=\frac{base_{1} +base_{2} }{2} h[/tex]
[tex]A=\frac{10+14}{2} *5\\A=12*5\\A=60[/tex]
Find distance between QB and HA
[tex]D=\sqrt{(x_{2} -x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}[/tex]
Q( -4,4) B (-2,9)
[tex]D=\sqrt{(-2--4)^{2}+(9-4)^{2} } \\D=\sqrt{2^{2} +5^{2} } \\D=\sqrt{29}[/tex]
Perimeter
[tex]P=10+14+2\sqrt{29} \\P=24 +2\sqrt{29} \\P= 24+10.77\\P=34.77[/tex]
