Question

a carpet is placed on a rectangular floor as shown in the diagram. find the area of the floor not covered by the carpet. 8 yd 1 yd 1 yd 1 yd 7 yd 1 yd

Explanation:

Step1: Calculate the area of the rectangular floor

The formula for the area of a rectangle is \(A = l\times w\). For the floor, \(l = 8\) yd and \(w=7\) yd. So, \(A_{floor}=8\times7 = 56\) \(yd^{2}\).

Step2: Calculate the dimensions and area of the carpet - covered region

The length of the carpet - covered region is \(l_{carpet}=8-(1 + 1)=6\) yd. The width of the carpet - covered region is \(w_{carpet}=7-(1 + 1)=5\) yd. Using the area formula \(A = l\times w\), \(A_{carpet}=6\times5=30\) \(yd^{2}\).

Step3: Calculate the area of the floor not covered by the carpet

Subtract the area of the carpet - covered region from the area of the floor. \(A = A_{floor}-A_{carpet}\). So, \(A = 56 - 30=26\) \(yd^{2}\).

Answer:

\(26\)