Question

1. magdalene is replacing part of a concrete walkway.

a. analyze and persevere describe how magdalene could decompose the area.
b. how many square feet of walkway is magdalene replacing?

Explanation:

Step1: Decompose the shape

Split the figure into a rectangle (top), a trapezoid (middle), and a rectangle (bottom).

Step2: Calculate top rectangle area

Area = length × width = $15 \times 3 = 45$ sq ft

Step3: Calculate bottom rectangle area

Area = length × width = $7 \times 3 = 21$ sq ft

Step4: Calculate trapezoid area

Trapezoid bases: 3 ft, 3 ft; height = 4 ft.
Area = $\frac{1}{2} \times (b_1 + b_2) \times h = \frac{1}{2} \times (3 + 3) \times 4 = 12$ sq ft

Step5: Sum all areas

Total area = $45 + 21 + 12$

Answer:

a. Magdalene can decompose the shape into two rectangles (top and bottom) and a trapezoid connecting them, then calculate each part's area and sum them.
b. 78 square feet