Question

what is the area of this figure?
9 cm
9 cm
5 cm
3 cm
4 cm
6 cm
square centimeters

Explanation:

Step1: Calculate area of large rectangle

The large rectangle has length 9 cm and width 6 cm? Wait, no, let's split the figure. Alternatively, consider the figure as a large square minus a small rectangle? Wait, no, better to split into two rectangles. First rectangle: length 9 cm, width 6 cm? Wait, no, the top part: length 9 cm, height 5 cm? Wait, no, let's look at the dimensions. The total height is 9 cm, the bottom part: from x=0 to x=6, y=0 to y=9-4=5? No, maybe better to split into two rectangles.

First rectangle: width 9 cm, height 5 cm? No, wait, the figure can be divided into a rectangle of 9 cm (length) and 6 cm (width) plus a rectangle of 3 cm (length) and 5 cm (height)? Wait, no, let's check the dimensions. The vertical side: total height 9 cm. The lower part: width 6 cm, height 9 - 5 = 4 cm? Wait, no, the right part: 3 cm (width) and 5 cm (height)? Wait, maybe another approach. The area of the figure can be calculated as the area of a 9x9 square minus the area of a 3x4 rectangle? Wait, no, 9x9 is 81, but the missing part is 3x4=12? Wait, no, let's check the coordinates.

Wait, the figure: the total width is 9 cm (since the top is 9 cm). The bottom part: from left to right, 6 cm, then 3 cm (so total 9 cm). The height: the top part is 5 cm, the bottom part is 4 cm (since 5 + 4 = 9). So we can split the figure into two rectangles:

1. Top rectangle: length 9 cm, height 5 cm. Area: 9 * 5 = 45 cm².

1. Bottom rectangle: length 6 cm, height 4 cm. Area: 6 * 4 = 24 cm².

Wait, but then the right part of the bottom: is there a rectangle? Wait, no, the bottom part: from x=0 to x=6, y=0 to y=4 (height 4 cm), and from x=6 to x=9 (width 3 cm), y=0 to y=5 cm? Wait, no, 5 + 4 = 9, so the bottom part (y=0 to y=4) is width 6 cm, and the right part (x=6 to x=9, y=0 to y=5) is width 3 cm, height 5 cm. Wait, that makes two rectangles:

• Rectangle 1: 9 cm (length) x 5 cm (height): 9*5=45.

• Rectangle 2: 6 cm (length) x 4 cm (height): 6*4=24.

Wait, but 95=45, 64=24, total 45+24=69? Wait, no, let's check another way. The area can also be calculated as the area of a 9x9 square minus the area of a 3x4 rectangle. Wait, 9x9=81, 3x4=12, 81-12=69. Yes, that matches. Because the missing part is a rectangle of 3 cm (width) and 4 cm (height), so subtracting that from the 9x9 square (which would be the case if the figure was a square with a 3x4 rectangle cut out). Let's verify:

Total area if it were a square: 9*9=81.

Missing area: 3*4=12.

So 81 - 12 = 69.

Alternatively, splitting into two rectangles:

Top rectangle: length 9 cm, height 5 cm: 9*5=45.

Bottom rectangle: length 6 cm, height 4 cm: 6*4=24.

Wait, but 95=45, 64=24, 45+24=69. Correct.

Or another split: left rectangle 6 cm (width) x 9 cm (height): 6*9=54.

Right rectangle 3 cm (width) x 5 cm (height): 3*5=15.

54+15=69. Yes, that works too.

So the area is 69.

Step1: Calculate area of 9x9 square

The square with side 9 cm has area $9 \times 9 = 81$ cm².

Step2: Calculate area of missing rectangle

The missing rectangle has length 3 cm and height 4 cm. Area: $3 \times 4 = 12$ cm².

Step3: Subtract missing area from square area

Total area: $81 - 12 = 69$ cm².

Answer:

69