Question

abbey is getting new carpet in her living room and hallway. the following diagram shows the two together. note: figure not drawn to scale. if a = 34 ft, b = 14 ft, c = 17 ft, and d = 18 ft, what is the area of the living room and hallway together? a. 166 ft² b. 83 ft² c. 374 ft² d. 782 ft²

Explanation:

Step1: Divide the shape into rectangles

We can divide the given shape into two rectangles. One rectangle has sides $c$ and $d$, and the other has sides $a - c$ and $d - b$.

Step2: Calculate area of first rectangle

The area of the first rectangle with length $c = 17$ ft and width $d=18$ ft is $A_1=c\times d=17\times18 = 306$ ft².

Step3: Calculate area of second rectangle

The length of the second rectangle is $a - c=34 - 17 = 17$ ft and the width is $d - b=18 - 14 = 4$ ft. So its area $A_2=(a - c)\times(d - b)=17\times4 = 68$ ft².

Step4: Calculate total area

The total area $A = A_1+A_2=306+68=374$ ft².

Answer:

C. 374 ft²