Question

what is the area of this figure?

Explanation:

Step1: Calculate the area of the first rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the rectangle with length \(l = 6\) ft and width \(w = 5\) ft, \(A_1=2\times5 = 10\) square - feet.

Step2: Calculate the area of the second rectangle

For the rectangle with length \(l=(2 + 6+3)\) ft and width \(w = 5\) ft. First, \(2+6 + 3=11\) ft. Then \(A_2=6\times11=66\) square - feet.

Step3: Calculate the area of the third rectangle

For the rectangle with length \(l = 6\) ft and width \(w = 3\) ft, \(A_3=6\times3 = 18\) square - feet.

Step4: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). Here \(b = 8\) ft and \(h=(6 + 5)\) ft. First, \(6+5 = 11\) ft. Then \(A_4=\frac{1}{2}\times8\times11=44\) square - feet.

Step5: Sum up the areas

\(A=A_1 + A_2+A_3+A_4\). Substitute the values: \(A=10 + 66+18+44\). \(A=138\) square - feet.

Answer:

The area of the figure is \(138\) square - feet.