Question

what is the area of this figure?
13 m
3 m
6 m
9 m
6 m
7 m
square meters

Explanation:

Step1: Split the figure into two rectangles

We can split the blue figure into a top rectangle and a bottom rectangle. The top rectangle has dimensions \(13\) m (length) and \(3\) m (height). The bottom rectangle has dimensions \(7\) m (length) and \(9\) m (height), but wait, actually, another way: or split into left and right? Wait, better to see: the top part is a rectangle with length \(13\) m and height \(3\) m. The bottom part: the total height is \(9\) m, so the height of the bottom rectangle (the vertical part) is \(9 - 3=6\) m? Wait, no, looking at the diagram, the bottom rectangle is \(7\) m in length and \(9\) m in height? Wait, no, maybe split into two rectangles: one is \(13\) m by \(3\) m, and the other is \(7\) m by \(9\) m? Wait, no, because there is a notch. Wait, actually, the correct split is: the figure can be divided into a rectangle of \(13\) m (length) and \(3\) m (height), and a rectangle of \(7\) m (length) and \(6\) m (height) (since \(9 - 3 = 6\)). Wait, let's check the dimensions. The horizontal length: the top rectangle is \(13\) m, the bottom rectangle: the length is \(7\) m, and the height is \(9\) m? Wait, no, maybe another approach: calculate the area of the large rectangle (if there was no notch) and subtract the area of the notch. The large rectangle would be \(13\) m by \(9\) m. The notch is a square (since \(6\) m by \(6\) m? Wait, the notch has length \(6\) m and height \(6\) m? Wait, the diagram shows: the top part is \(3\) m height, \(13\) m length. Then, below that, on the left, there is a notch with length \(6\) m and height \(6\) m (since \(9 - 3 = 6\)). So the area of the figure is the area of the large rectangle (\(13\times9\)) minus the area of the notch (\(6\times6\)). Let's verify:

Step2: Calculate area of large rectangle (without notch)

Area of large rectangle: \(13\times9 = 117\) square meters.

Step3: Calculate area of the notch

The notch is a rectangle with length \(6\) m and height \(6\) m (since the horizontal length of the notch is \(6\) m, and vertical height is \(9 - 3 = 6\) m). So area of notch: \(6\times6 = 36\) square meters.

Step4: Subtract notch area from large rectangle area

Area of the figure: \(117 - 36 = 81\)? Wait, no, that can't be. Wait, maybe my split is wrong. Let's try another way. Let's split the figure into two rectangles:

First rectangle: top part, length \(13\) m, height \(3\) m. Area: \(13\times3 = 39\) square meters.

Second rectangle: bottom part, length \(7\) m, height \(9\) m? Wait, no, because the bottom part's length: the total length is \(13\) m, but the bottom rectangle is \(7\) m in length (as per the diagram: the right part is \(7\) m). Wait, the bottom rectangle is \(7\) m (length) and \(9\) m (height), and the left part (the vertical part) is \( (13 - 7) \) m? Wait, \(13 - 7 = 6\) m. So the left part of the bottom: length \(6\) m, height \(6\) m (since \(9 - 3 = 6\))? No, this is getting confusing. Let's use the correct split:

Looking at the diagram, the figure can be divided into two rectangles:

1. Top rectangle: length = \(13\) m, height = \(3\) m. Area = \(13 \times 3 = 39\) m².

2. Bottom rectangle: length = \(7\) m, height = \(9\) m. Wait, no, because the bottom rectangle's height is \(9\) m, and length is \(7\) m. But then, the total area would be \(39 + (7\times9) = 39 + 63 = 102\)? Wait, that doesn't seem right. Wait, maybe the bottom rectangle is \(7\) m (length) and \(6\) m (height) (since \(9 - 3 = 6\)), and the top is \(13\) m (length) and \(3\) m (height). Then area of bottom rectangle: \(7\times6 = 42\), top: \(13\times3 = 39\), total \(39 + 42 = 81\)? No, that's conflicting. Wait, let's look at the dimensions again. The vertical side on the right is \(9\) m. The horizontal side at the bottom is \(7\) m. The horizontal side at the top is \(13\) m. The vertical side on the left of the notch is \(6\) m (since \(9 - 3 = 6\)), and the horizontal side of the notch is \(6\) m. So the area of the figure is:

Area = (Area of top rectangle) + (Area of bottom rectangle)

Top rectangle: length = \(13\) m, height = \(3\) m. Area = \(13 \times 3 = 39\) m².

Bottom rectangle: length = \(7\) m, height = \(9\) m? No, because the bottom rectangle's length is \(7\) m, and its height is \(9\) m, but the top rectangle is \(13\) m, so the overlapping? Wait, no, the correct way is: the figure is composed of a rectangle with length \(13\) m and height \(3\) m, and a rectangle with length \(7\) m and height \(6\) m (since \(9 - 3 = 6\)). Wait, \(13\) m length for the top, and the bottom rectangle: the length is \(7\) m, and the height is \(6\) m. Then total area is \(13\times3 + 7\times6\). Let's calculate that:

\(13\times3 = 39\), \(7\times6 = 42\), so \(39 + 42 = 81\). Wait, but another way: the large rectangle (if no notch) is \(13\) m by \(9\) m, area \(13\times9 = 117\). The notch is a rectangle with length \(6\) m (since \(13 - 7 = 6\)) and height \(6\) m (since \(9 - 3 = 6\)), so area \(6\times6 = 36\). Then \(117 - 36 = 81\). Yes, that matches. So the area is \(81\) square meters. Wait, but let's check again. Wait, the notch: the horizontal length of the notch is \(13 - 7 = 6\) m, and the vertical height of the notch is \(9 - 3 = 6\) m. So the notch is a square with side \(6\) m. So area of large rectangle: \(13\times9 = 117\). Area of notch: \(6\times6 = 36\). So area of figure: \(117 - 36 = 81\).

Wait, but let's confirm with the split into two rectangles. First rectangle: top, \(13\) m by \(3\) m: area \(39\). Second rectangle: bottom, \(7\) m by \(9\) m? No, that would be \(63\), total \(102\), which is wrong. So the mistake is in the second rectangle. The correct second rectangle is \(7\) m by \(6\) m (since the height from the bottom to the top of the second rectangle is \(9 - 3 = 6\) m). So \(7\times6 = 42\). Then \(39 + 42 = 81\). Yes, that's correct. So the area is \(81\) square meters.

Answer:

\(81\)