Question

use formulas to find the area of the figure.
26 in.
6 in.
19 in.
6 in.
a. 166 in.²
b. 122 in.²
c. 187 in.²
d. 270 in.²

Explanation:

Step1: Split the figure into two rectangles

The T - shaped figure can be divided into a top rectangle and a bottom rectangle. The top rectangle has length \( l_1 = 26\) in and width \( w_1=6\) in. The bottom rectangle has length \( l_2 = 6\) in and width \( w_2 = 19\) in.

Step2: Calculate the area of the top rectangle

The formula for the area of a rectangle is \( A=\text{length}\times\text{width}\). For the top rectangle, \( A_1=l_1\times w_1=26\times6 = 156\) square inches.

Step3: Calculate the area of the bottom rectangle

For the bottom rectangle, using the area formula \( A = \text{length}\times\text{width}\), we have \( A_2=l_2\times w_2=6\times19=114\) square inches. Wait, no, that's a mistake. Wait, actually, the bottom rectangle's width is 19? Wait, no, looking at the figure again, the bottom rectangle has width 19? Wait, no, maybe I split it wrong. Wait, the correct split: the top rectangle is 26 in long and 6 in wide, and the bottom rectangle is 6 in long and 19 in wide? Wait, no, that can't be. Wait, maybe the bottom rectangle has length 6 and height 19, and the top rectangle has length 26 and height 6. Wait, but when we calculate the total area, we can also think of the figure as the sum of two rectangles: one with dimensions \( 26\times6\) and another with dimensions \( 6\times19\)? Wait, no, that would be wrong. Wait, no, actually, the correct way: the T - shape, the horizontal part is 26 in (length) and 6 in (height), and the vertical part is 6 in (length) and 19 in (height). But when we add their areas, we have to make sure there is no overlap. Wait, actually, the correct calculation: \( A=26\times6 + 6\times19\)? Wait, no, that gives \( 156+114 = 270\)? Wait, but let's check again. Wait, maybe the bottom rectangle's length is 6, and the top rectangle's length is 26, and the height of the top is 6, height of the bottom is 19. Then \( A=26\times6+6\times19=156 + 114=270\) square inches.

Answer:

D. \(270\space\text{in}^2\)