Exercise 10 Page 435

Let's start with marking the vertices and drawing the polygon in a coordinate plane.

The polygon is a quadrilateral.

Perimeter

Three of its sides are parallel to one of the axes so we can determine their lengths by counting the number of squares between the points.

To find the length of the last side of the quadrilateral we have to use the Distance Formula.

The last side is around 6.3 units.

The perimeter of the polygon is therefore approximately 6+6+4+6.3=22.3.

Area

To determine the area we divide the polygon into a rectangle and a triangle.

The area of a rectangle is the product of the base and height: A_(rectangle)=6*4 = 24. The area of a triangle is the product of the base and height divided by 2: A_(triangle)=6*2/2=6. Thus, the area of the polygon is A_(polygon)=24+6 = 30.