Question

what is the area of this figure?
9 mi
2 mi
6 mi
6 mi
4 mi
15 mi
square miles
submit

Explanation:

Step1: Divide the figure into two rectangles

We can split the composite figure into a left rectangle and a right rectangle. The left rectangle has length 9 mi and height 6 mi. The right rectangle has length 6 mi and height 4 mi. Alternatively, we can also consider another way: the total length is 15 mi, and we can find the area by subtracting the missing part or adding two rectangles. Let's use the method of adding two rectangles. The first rectangle: length = 9 mi, height = 6 mi. The second rectangle: length = 6 mi, height = 4 mi. Wait, actually, another way: the vertical side on the left is 6 mi, and the vertical side on the right is 4 mi, so the difference is 6 - 4 = 2 mi, which is the height of the small rectangle on top of the right part. Wait, maybe a better way: the figure can be divided into a large rectangle of 15 mi (length) and 4 mi (height), and a small rectangle of 9 mi (length) and (6 - 4) = 2 mi (height). Let's check that.

Step2: Calculate the area of the large rectangle

The large rectangle has length \( 15 \) mi and height \( 4 \) mi. The area of a rectangle is \( \text{length} \times \text{height} \), so the area is \( 15 \times 4 = 60 \) square miles.

Step3: Calculate the area of the small rectangle

The small rectangle has length \( 9 \) mi and height \( (6 - 4) = 2 \) mi. The area is \( 9 \times 2 = 18 \) square miles.

Step4: Add the two areas together

To find the total area of the figure, we add the area of the large rectangle and the area of the small rectangle: \( 60 + 18 = 78 \) square miles.

Alternatively, we can calculate the area by dividing into two rectangles: first rectangle (left) with length 9 mi and height 6 mi: \( 9 \times 6 = 54 \) square miles. Second rectangle (right) with length 6 mi and height 4 mi: \( 6 \times 4 = 24 \) square miles. Then total area is \( 54 + 24 = 78 \) square miles. Both methods give the same result.

Answer:

78