Question

find the perimeter and area.
1
p =
a =

Explanation:

Step1: Calculate the perimeter

The perimeter of a shape is the sum of all its side - lengths.
By moving the sides (using the property of translation), we can find that the perimeter \(P\) is equal to the perimeter of a rectangle with length \(l = 6\) yd and width \(w=3\) yd.
The formula for the perimeter of a rectangle is \(P = 2(l + w)\).
Substitute \(l = 6\) and \(w = 3\) into the formula:
\(P=2\times(6 + 3)=2\times9 = 18\) yd.

Step2: Calculate the area

The area of the composite shape can be found by splitting it into two parts.
One part is a rectangle with length \(l_1=2\) yd and width \(w_1 = 3\) yd, and the area \(A_1=l_1\times w_1=2\times3 = 6\) yd².
The second part is a trapezoid. The bases of the trapezoid are \(b_1 = 3\) yd and \(b_2=2\) yd, and the height \(h=(6-(2 + 2))=2\) yd. The formula for the area of a trapezoid is \(A_{t}=\frac{(b_1 + b_2)h}{2}\).
\(A_{t}=\frac{(3 + 2)\times2}{2}=5\) yd².
The third part is a rectangle with length \(l_2=2\) yd and width \(w_2 = 2\) yd, and the area \(A_2=l_2\times w_2=2\times2 = 4\) yd².
The total area \(A=A_1+A_{t}+A_2=6 + 5+4=15\) yd².

Answer:

\(P = 18\) yd, \(A=15\) yd²