Question

2
5 cm
9 cm
4 cm
2 cm
p =
a =

Explanation:

Step1: Calculate the perimeter

The perimeter of a shape is the sum of all its sides. For this irregular shape, we can use the property that the perimeter of an irregular polygon (with right - angles) is the same as the perimeter of a rectangle with length \(l = 9\space cm\) and width \(w = 5\space cm\).
The formula for the perimeter of a rectangle is \(P=2(l + w)\).
Substitute \(l = 9\space cm\) and \(w = 5\space cm\) into the formula:
\(P=2\times(9 + 5)=2\times14 = 28\space cm\)

Step2: Calculate the area

We can split the shape into two rectangles.

• First rectangle:

Let the first rectangle have length \(l_1=(9 - 4)=5\space cm\) and width \(w_1 = 5\space cm\). The area of a rectangle is \(A=\text{length}\times\text{width}\), so \(A_1=5\times5 = 25\space cm^{2}\)

• Second rectangle:

The second rectangle has length \(l_2 = 4\space cm\) and width \(w_2=2\space cm\). So \(A_2=4\times2=8\space cm^{2}\)

The total area \(A=A_1 + A_2\)
\(A=25+8=33\space cm^{2}\)

Answer:

\(P = 28\space cm\), \(A=33\space cm^{2}\)