Question

find the perimeter and area of the figure pictured below. 2.8 m 11.6 m 3.3 m 9.1 m perimeter = m area = m² question help: video 1 video 2 post to forum

Explanation:

Step1: Calculate the perimeter

The perimeter of the figure is the sum of all its outer - side lengths. Using the property that we can translate the inner sides to form a rectangle. The formula for the perimeter of a rectangle is \(P = 2\times(\text{length}+\text{width})\). Here, length \(l=11.6\) m and width \(w = 9.1\) m.
\(P=2\times(11.6 + 9.1)=2\times20.7 = 41.4\) m.

Step2: Calculate the area

We can split the figure into two rectangles.
First rectangle: length \(l_1=11.6\) m, width \(w_1 = 2.8\) m. Area \(A_1=l_1\times w_1=11.6\times2.8=32.48\) \(m^{2}\).
Second rectangle: length \(l_2=9.1 - 2.8=6.3\) m, width \(w_2 = 3.3\) m. Area \(A_2=l_2\times w_2=6.3\times3.3 = 20.79\) \(m^{2}\).
Total area \(A=A_1 + A_2=32.48+20.79=53.27\) \(m^{2}\).

Answer:

Perimeter \(=41.4\) m, Area \(=53.27\) \(m^{2}\)