Question

What is the area of the polygon

Answer 1

Look at the picture.

`A_I=(7\cdot2)/(2)=7\\\\A_(II)=(4\cdot3)/(2)=6\\\\A_(III)=(7\cdot3)/(2)=10.5\\\\A_(IV)=3\cdot4=12\\\\The\ area\ of\ the\ polygon\\\\A=A_I+A_(II)+A_(III)+A_(IV)\\\\A=7+6+10.5+12=35.5\ un^2`

Answer 2

split this figure into 3 shapes: 2 triangles and 1 trapezoid

Area of top triangle = 1/2(7)(2) = 7 square units
Area of bottom triangle = 1/2(3)(7) = 10.5 square units
Area of trapezoid = 1/2(3 + 6)(4) = 18 square units

Area of the polygon = 7 + 10.5 + 18 = 35.5 square units