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

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:

$A1=L^2$

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

$\displaystyle A2=\frac{b1+b2}{2}h$

Calculate both areas:

$A1=2^2=4$

$\displaystyle A2=\frac{2+4}{2}\cdot 1=3$

Total Area=4+3=7

The area of the polygon CDEFGH is 7