Exercise 129 Page 139

To calculate the area of the trapezoid, we add the length of the parallel sides, multiply by the height, and divide by 2. A_((4))=1/2(4)(5+2)=14 units^2 [1em] Finally, we will add the area of the four shapes to obtain the area of the original figure. 6+9/2+15/2+14 = 32 units^2

Perimeter

To calculate the perimeter we need to know the length of the polygon's sides. Using the Pythagorean Theorem, we can identify three of the unknown sides. |c|c|c| [-0.7em] Triangle & a^2+b^2=c^2 & Solve for c [0.4em] [-0.7em] (1) & 3^2+4^2=c^2 & 5 units [0.5em] [-0.7em] (2) & 3^2+3^2=c^2 & 3sqrt(2) units [0.4em] [-0.7em] (3) & 3^2+5^2=c^2 & sqrt(34) units [0.4em] To calculate the last side of the polygon we will add some information to the diagram.

To calculate the remaining side we need to use the Pythagorean Theorem once more. However, notice that this triangle has the same pair of legs as triangle 1. Therefore, we know that the remaining side of the polygon must be 5 units as well.

Now we can calculate the shape's perimeter. 5+3sqrt(2)+sqrt(34)+5≈ 20 units

|c|c|c| [-0.7em] Rectangle & wl & Area [0.4em] [-0.7em] (1) & (4)(5) & 20 units^2 [0.5em] [-0.7em] (2) & (1)(2) & 2 units^2 [0.5em] [-0.7em] (3) & (1)(2) & 2 units^2 [0.5em] [-0.7em] (4) & (3)(4) & 6 units^2 [0.5em] Finally, we will add the area of the rectangles to obtain the area of the original figure. 20+2+2+6 = 30 units^2 To determine the perimeter, we have to add the length of the polygon's sides. Notice that we have two sides that are 4 units long, two sides that are 3 units long, four sides that are 2 units long, and finally three sides with a length of 1 unit. 2(4)+2(3)+4(2)+3(1)+5= 30 units