Question

Find the area A of polygon CDEFGH with the given vertices. C(0,5), D(2,5), E(2,3), F(3,2), G(-1,2), H(0,3)

Answer 1

The area of the polygon CDEFGH is 7

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:

`A1=L^2`

The area HEFG is a trapezoid with bases lengths 4 and 2, and height 1. Area of a trapezoid:

`\displaystyle A2=(b1+b2)/(2)h`

Calculate both areas:

`A1=2^2=4`

`\displaystyle A2=(2+4)/(2)\cdot 1=3`

Total Area=4+3=7

The area of the polygon CDEFGH is 7