Question

a house 25 m by 9 m is surrounded by a walkway 1.6 m wide. a) find the area of the region covered by the house and the walkway. b) find the area of the walkway.

Explanation:

Step1: Calculate outer - length and width

The length of the house with the walkway is $25 + 2\times1.6=25 + 3.2 = 28.2$ m. The width of the house with the walkway is $9+2\times1.6 = 9 + 3.2=12.2$ m.

Step2: Calculate area of house and walkway

The area of a rectangle is $A = l\times w$. So the area of the region covered by the house and the walkway is $A_1=28.2\times12.2 = 344.04$ m².

Step3: Calculate area of the house

The area of the house is $A_2 = 25\times9=225$ m².

Step4: Calculate area of the walkway

The area of the walkway is the area of the house and walkway minus the area of the house. So $A = A_1 - A_2=344.04 - 225 = 119.04$ m².

Answer:

a) $344.04$ m²
b) $119.04$ m²