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: Find outer - length and width

The length of the house with walkway is $l = 25+2\times1.6=25 + 3.2=28.2$ m. The width of the house with walkway is $w = 9+2\times1.6=9 + 3.2 = 12.2$ 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 $A_1=28.2\times12.2 = 344.04$ $m^{2}$.

Step3: Calculate area of the house

The area of the house is $A_2=25\times9=225$ $m^{2}$.

Step4: Calculate area of the walkway

The area of the walkway is $A = A_1 - A_2$. So $A=344.04−225 = 119.04$ $m^{2}$.

Answer:

a) $344.04$ $m^{2}$
b) $119.04$ $m^{2}$