Question

what is the area of the object shown?
a. 272 sq in
b. 228 sq in
c. 168 sq in
d. 248 sq in

Explanation:

Step1: Divide the shape into two rectangles

We can divide the given shape into a rectangle with dimensions 12 in by 10 in and another rectangle with dimensions 8 in by 6 in.

Step2: Calculate the area of the first rectangle

The area formula for a rectangle is $A = l\times w$. For the first rectangle with length $l = 12$ in and width $w = 10$ in, $A_1=12\times10 = 120$ square - inches.

Step3: Calculate the area of the second rectangle

For the second rectangle with length $l = 8$ in and width $w = 6$ in, $A_2=8\times6=48$ square - inches.

Step4: Calculate the area of the combined shape

The area of the combined shape $A = A_1+(20 - 12)\times10$. First, we note that the second part of the large - shaped area (besides the first rectangle) has a base of $20 - 12=8$ in and height of 10 in. So $A=120 + 8\times10=120+80 = 200+48=248$ square - inches.

Answer:

D. 248 sq in