A house 32 m by 9 m is surrounded by a walkway 1.3 m wide. a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway. a) The area of the region covered by the building and the walkway is \( \square \mathrm{m}^{2} \). (Round to the nearest whole number as needed.)

To find the area of the region covered by the house and the walkway, first, we need to calculate the dimensions of the entire area including the walkway. The house measures 32 m by 9 m, and with the walkway of 1.3 m surrounding it, we add twice the width of the walkway to each dimension: Length: \(32\,m + 2(1.3\,m) = 32\,m + 2.6\,m = 34.6\,m\) Width: \(9\,m + 2(1.3\,m) = 9\,m + 2.6\,m = 11.6\,m\) Now, calculate the area: \[ \text{Area of the house and walkway} = 34.6\,m \times 11.6\,m = 401.36\, m^{2} \] Rounding to the nearest whole number, we get \(401\,m^{2}\). For the area of the walkway, we first calculate the area of the house alone: \[ \text{Area of the house} = 32\,m \times 9\,m = 288\,m^{2} \] Then, we find the area of the walkway by subtracting the area of the house from the total area covered by the house and the walkway: \[ \text{Area of the walkway} = \text{Area of house and walkway} - \text{Area of house} = 401\,m^{2} - 288\,m^{2} = 113\,m^{2} \] So, the area of the walkway is \(113\,m^{2}\).