Question

what is the area of this figure? 8 mi 7 mi 9 mi 2 mi 2 mi 6 mi square miles submit

Explanation:

Step1: Area of large rectangle

The large rectangle (if we consider the full height as 9 mi and width as 8 mi) would have area, but actually, we can split the figure. Alternatively, calculate the area of the main part and adjust for the missing square. First, let's find the area of the rectangle with length 8 mi and height 9 mi, then subtract the area of the missing square. Wait, no, maybe better to split into two rectangles. Wait, the figure has a notch. Let's see: the bottom part: width is 6 mi, height is (9 - 2) = 7 mi? Wait, no. Wait, the left side: 7 mi, then a notch of 2 mi down and 2 mi right. So another way: the area can be calculated as the area of the rectangle with length 8 mi and height 7 mi, plus the area of the rectangle with length 6 mi and height 2 mi. Wait, let's check dimensions. The top part: width 8 mi, height 7 mi (since total height is 9, and the bottom part is 2 mi height). Then the bottom part: width 6 mi, height 2 mi. So area1 = 87 = 56, area2 = 62 = 12, total area = 56 + 12 = 68? Wait, no, maybe another approach. Alternatively, the figure can be seen as a large rectangle of 8 mi (width) and 9 mi (height) minus a square of 2 mi (since the notch is 2x2). Wait, 8*9 = 72, then the notch is 2x2=4, so 72 - 4 = 68? Wait, let's verify. The large rectangle: length 8, height 9: area 72. The missing part is a square with side 2 (since the horizontal notch is 2 mi, and vertical is 2 mi). So 72 - 4 = 68. Yes, that makes sense.

Step1: Calculate area of large rectangle

Large rectangle: length = 8 mi, height = 9 mi. Area = length * height = $8 \times 9 = 72$ square miles.

Step2: Calculate area of the missing square

The missing part is a square with side length 2 mi. Area of square = side * side = $2 \times 2 = 4$ square miles.

Step3: Subtract to get the area of the figure

Area of figure = Area of large rectangle - Area of missing square = $72 - 4 = 68$ square miles.

Answer:

68