Question

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

Explanation:

Step1: Divide the figure into rectangles

Divide the given figure into three rectangles.

Step2: Calculate the area of each rectangle

• For the first rectangle (top - right): Area $A_1 = 3\times4=12\ \text{ft}^2$ (using the formula $A = l\times w$, where $l = 4\ \text{ft}$ and $w = 3\ \text{ft}$).
• For the second rectangle (middle): The width is $2 + 3+2-(3 + 3)=1\ \text{ft}$ (by analyzing the horizontal side lengths). But another way: The combined length of the two non - top and non - bottom rectangles in the vertical direction is $4 + 4=8\ \text{ft}$ and the width (horizontal) for the middle part (calculated as $2+(3 + 3)-(3 + 3)=2\ \text{ft}$). Wait, better approach: The figure can be considered as two rectangles of $4\times(2 + 3+2)$ and $4\times3$. Wait, no. Correct approach:

The figure can be split into three rectangles. The two side rectangles (top and bottom) each have dimensions $4\times3$ and the middle rectangle has dimensions $4\times(2 + 2)$.

• Area of the two side rectangles (top and bottom): Each has area $A_{side}=4\times3$, and there are two of them, so $A_{side - total}=2\times4\times3 = 24\ \text{ft}^2$
• Area of the middle rectangle: $A_{middle}=4\times(2 + 2)=12\ \text{ft}^2$ (length $4\ \text{ft}$ and width $2+2 = 4\ \text{ft}$)

Step3: Sum up the areas

$A=A_{side - total}+A_{middle}=24 + 12=36\ \text{ft}^2$

Answer:

$36\ \text{ft}^2$