Question

find the area of the figure. (sides meet at right angles.) 2 in 2 in 2 in 2 in 5 in 5 in 5 in in 2

Explanation:

Step1: Calculate the area of the lower rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the lower rectangle, length \(l = 5\) in and width \(w = 5\) in. So, \(A_1=5\times5 = 25\) \(in^2\).

Step2: Calculate the area of the upper rectangle

The length of the upper rectangle: \(l=(5 - 2-2)+2 + 2=7\) in (by adding the non - overlapping parts and the two 2 - in segments), width \(w = 2\) in. Using the area formula \(A = l\times w\), \(A_2=7\times2=14\) \(in^2\).

Step3: Sum the areas of the two rectangles

The total area \(A=A_1 + A_2\). Substitute \(A_1 = 25\) \(in^2\) and \(A_2=14\) \(in^2\) into the formula. So, \(A=25 + 14=39\) \(in^2\).

Answer:

\(39\) \(in^2\)