Question

a diagram of ryans yard is shown. which expression can ryan use to find the total area of his yard? a. (10 + 4)×(12 + 5) b. (10 + 4)×(12 - 5) c. (12×10)-(5×4) d. (12×10)+(5×4)

Explanation:

Step1: Divide the figure into rectangles

We can consider the yard as a large rectangle with a smaller rectangle cut - out. The large rectangle has dimensions \(14\) ft by \(12\) ft and the smaller rectangle (the cut - out part) has dimensions \(4\) ft by \(5\) ft. Another way is to split the figure into two non - overlapping rectangles. One rectangle has dimensions \(10\) ft by \(12\) ft and the other has dimensions \(4\) ft by \(5\) ft.

Step2: Calculate the area using the sum of rectangle areas

The area of a rectangle is given by \(A = l\times w\) (length times width). The total area of the yard is the sum of the areas of the two non - overlapping rectangles. The area of the first rectangle with length \(l_1 = 10\) ft and width \(w_1 = 12\) ft is \(A_1=10\times12\). The area of the second rectangle with length \(l_2 = 4\) ft and width \(w_2 = 5\) ft is \(A_2 = 4\times5\). The total area \(A=A_1 + A_2=(12\times10)+(5\times4)\)

Answer:

D. \((12\times10)+(5\times4)\)