Answer:
The area of the polygon CDEFGH is 7
Step-by-step explanation:
Area of a Polygon
The area of a polygon is generally calculated as the sum of the smaller areas that form its full shape, give each partial area has a known shape, like a square, rectangle, triangle, circle, etc.
The six points given in the question are plotted in the image below. They form a polygon whose area can be divided into two smaller shapes:
The area CDHE is a square of length side 2. Area of a square:
[tex]A1=L^2[/tex]
The area HEFG is a trapezoid with bases lengths 4 and 2, and height 1. Area of a trapezoid:
[tex]\displaystyle A2=\frac{b1+b2}{2}h[/tex]
Calculate both areas:
[tex]A1=2^2=4[/tex]
[tex]\displaystyle A2=\frac{2+4}{2}\cdot 1=3[/tex]
Total Area=4+3=7
The area of the polygon CDEFGH is 7
