Question

How do you solve the area of this polygon?

Answer 1

The top side and the bottom side are parallel.
The polygon is a trapezoid.
The area of a trapezoid is A = (B + b)h/2, where B and b are the lengths of the bases (the parallel sides) and h is the height of the trapezoid.
The height of a trapezoid is a segment that is perpendicular to the bases and whose endpoints are on the bases.
In the figure, the leftmost vertical segment is the height of the trapezoid.
We need to find its length.
The leftmost vertical segment is a leg of a right triangle. The other leg is the 10 m segment on top. The hypotenuse is the diagonal segment. That diagonal segment measures 26 m like the one on the right side.
For the right triangle, we have a^2 + b^2 = c^2.
a^2 + 10^2 = 26^2
a^2 = 576
a = 24
The height of the trapezoid is 24 m.
The lower base of the trapezoid has length 40 m + 20 m = 60 m.
The upper base of the trapezoid has length 10 m + 40 m = 50 m.
Since we know the bases and height of the trapezoid, we can calculate its area using the formula above.

A = (B + b)h/2 = (60 m + 50 m)(24 m)/2 = 1320 m^2