Question

eva made a rectangular mattress pad out of material that covered the top and sides of the mattress. how much fabric did eva use to cover the top and sides of the mattress? 20 ft² 21 ft² 41 ft² 62 ft²

Explanation:

Step1: Calculate the area of the top

The area of the top is length × width. Given length \(l = 3\) ft and width \(w=7\) ft. So, \(A_{top}=3\times7 = 21\) \(ft^{2}\)

Step2: Calculate the area of the two side - faces with dimensions \(1\times3\)

The area of one face with dimensions \(1\times3\) is \(A_{1}=1\times3\). There are two such faces. So, \(A_{s1}=2\times(1\times3)=6\) \(ft^{2}\)

Step3: Calculate the area of the two side - faces with dimensions \(1\times7\)

The area of one face with dimensions \(1\times7\) is \(A_{2}=1\times7\). There are two such faces. So, \(A_{s2}=2\times(1\times7) = 14\) \(ft^{2}\)

Step4: Calculate the total fabric area

The total fabric area \(A=A_{top}+A_{s1}+A_{s2}\). Substitute the values: \(A = 21+6 + 14=41\) \(ft^{2}\)

Answer:

\(41\ ft^{2}\) (the third option)