Question

geometry, measurement, data analysis
areas of a piecewise rectangular figure
find the area of the figure. (sides meet at right angles.)

Explanation:

Step1: Divide the figure into rectangles

We can divide the given figure into two rectangles. One rectangle has dimensions \(4 + 4+4=12\) ft (length) and \(4\) ft (width), and the other has dimensions \(4\) ft (length) and \(3\) ft (width).

Step2: Calculate area of first rectangle

The area formula for a rectangle is \(A = l\times w\). For the first rectangle with \(l = 12\) ft and \(w = 4\) ft, \(A_1=12\times4 = 48\) square - feet.

Step3: Calculate area of second rectangle

For the second rectangle with \(l = 4\) ft and \(w = 3\) ft, \(A_2 = 4\times3=12\) square - feet.

Step4: Calculate total area

The total area \(A\) of the figure is the sum of the areas of the two rectangles, \(A=A_1 + A_2=48+12 = 60\) square - feet.

Answer:

60