What is the area of this polygon? 42.5 units² 41.5 units² 35.5 units² 29.5 units²

Area of polygon is:

39 square units.

Step-by-step explanation:

The area of polygon is equal to:

Area of ΔBAF+Area of ΔFGC+Area of ΔAEF+Area of rectangle EFGD.

Firstly we will draw a perpendicular from point B to side  which is the base(b)=7 units. to obtain the height(h)=3 units

Area of ΔBAF= (1/2)×b×h

                     =(1/2)×7×3=21/2 square units(1)

Also in ΔFGC:

Base(b)=FG=4 units

and height(h)=GC=3 units.

Area of ΔFGC=(1/2)×b×h

                      =(1/2)×4×3

                     =6 square units(2)

In ΔAEF:

Base(b)=7 units.

Height(h)=FE=3 units.

Area of ΔAEF=(1/2)×7×3

                      =21/2 square units(3)

Now in rectangle  EFGD:

Length(l)=ED=4 units

Breadth(b)=DG=3 units

Area of  rectangle  EFGD=l×b

                                        =4×3

                                        =12 square units(4)

Hence, Area of Polygon is: (1)+(2)+(3)+(4)

Hence, The area of Polygon is:

39 square units.

0.038

step-by-step explanation: