Question

incorrect
your answer is incorrect.
find the area of the shape.
(sides meet at right angles.)
diagram with measurements: 2 in, 2 in, 2 in, 3 in, 6 in, 2 in, 1 in, 2 in (note: last 2 m likely typo, should be 2 in)

Explanation:

Step1: Divide the shape into rectangles

We can divide the L - shaped figure into three rectangles. Let's identify their dimensions:

• Rectangle 1: Width = 2 in, Height = 2 in. Area formula: $A = l\times w$. So area $A_1=2\times2 = 4$ square inches.
• Rectangle 2: Width = 2 + 2=4 in, Height = 3 in. Area $A_2 = 4\times3=12$ square inches.
• Rectangle 3: Width = 2 in, Height = 1 in. Area $A_3=2\times1 = 2$ square inches.

Step2: Sum the areas of the rectangles

Total area $A=A_1 + A_2+A_3$. Substitute the values: $A = 4+12 + 2=18$ square inches.

(Alternative way: Another way is to use the big rectangle minus the missing parts, but the division method is more straightforward here. Let's verify with the big rectangle: The overall width if we consider the base is 2 + 2+ 2=6 in? Wait, no, the height is 6 in. Wait, maybe my first division was wrong. Let's re - divide:

Alternative Step1: Divide into three rectangles correctly.

• Top rectangle: width = 2 in, height = 2 in. Area $A_1 = 2\times2=4$.
• Middle rectangle: width = 2 + 2 = 4 in, height = 3 in. Area $A_2=4\times3 = 12$.
• Bottom rectangle: width = 2 in, height = 1 in. Area $A_3=2\times1=2$. Wait, but let's check the total height: 2 + 3+1=6 in, which matches the right - hand side height. The total width: the right - most part is 2 in, the middle part (horizontal) is 2 in, and the left - most part (horizontal) is 2 in. So the total width is 2+2 + 2=6 in? Wait, no, the vertical sides: the right - hand side is 6 in. Let's use another method. The shape can be seen as a combination of three rectangles:

1. Top rectangle: 2 in (width) $\times$ 2 in (height) = 4.
2. Middle rectangle: (2 + 2) in (width) $\times$ 3 in (height)=4×3 = 12.
3. Bottom rectangle: 2 in (width) $\times$ 1 in (height)=2.

Summing them: 4 + 12+2 = 18.

Or, we can calculate the area as the area of the large rectangle (if we extend the sides) minus the area of the missing parts. The large rectangle would have dimensions 6 in (height) and (2 + 2+2)=6 in (width)? No, wait, the horizontal length: from the bottom, the right - most is 2 in, then moving left, there is a 2 in segment, then another 2 in segment. So total horizontal length is 2+2 + 2=6 in. The vertical length is 6 in. But the shape is not a square, because there are indentations? Wait, no, the given shape has sides meeting at right angles. Let's count the squares or use the grid method. Wait, maybe my initial division was correct. Let's check the coordinates. Let's place the bottom - right corner at (0,0). Then:

• Bottom rectangle: from (0,0) to (2,1). Area = 2×1 = 2.
• Middle rectangle: from (0,1) to (4,4) (since height from 1 to 4 is 3, width from 0 to 4 is 2 + 2). Area = 4×3 = 12.
• Top rectangle: from (2,4) to (4,6) (width 2, height 2). Area = 2×2 = 4.

Summing these: 2+12 + 4=18.

Answer:

18 square inches