How do I find area of this polygon?

Area = 297cm²

Step-by-step explanation:

Let Polygon be ABCDE

Draw a line CE parallel to AB which make right angles at F.

now, CE = AB

also, CF = FE = 22 / 2 = 11cm

and the line drawn from the vertex of the D = 19cm to G on AB.

AE = BC = FG = 8cm

so, FD = 19 - 8 = 11cm

Now the Area.

Area of the polygon = Area of the Rectangle ABCE + 2 x Area of either Triangle

(we need not calculate both the area of triangle as two sides of the triangle is equal)

Area of the Rectangle ABCE = l x b

here l = 22 cm and b = 8cm

= 22 x 8 = 176cm²      ---------------(i)

2 x Area of either Triangle = 2 x 1/2 x b x h

here, b(CF or EF) = 11cm and h(FD) = 11cm

= 11 x 11 = 121cm²        ----------------(ii)

Area of the polygon = Area of the Rectangle ABCE + 2 x Area of either Triangle

From (i) and (ii),

Area = 176 + 121

Area = 297cm²