Question

what is the area of this figure?
7 in
4 in
4 in
9 in
5 in
2 in
6 in
8 in
8 in
3 in
square inches

Explanation:

Step1: Split figure into 3 rectangles

Divide the shape into three separate rectangles: top-left, top-right, bottom.

Step2: Calculate area of top-left rect

Find height: $9 - 4 = 5$ in. Area: $7 \times 9 = 63$? No, correct: top-left is $7$ in wide, height $9-4=5$? No, recheck: top-left is $7$ in width, total height $9$ in, minus the 4 in indent? No, better: top-left rectangle: width $7$ in, height $9 - 5 = 4$ in? No, split correctly:

1. Top-left: $7$ in $\times (9 - 4) = 7 \times 5 = 35$ in²
2. Top-right: $4$ in $\times 5$ in $= 20$ in²
3. Bottom: $3$ in $\times 8$ in $= 24$ in²

Wait, no, the middle section: total bottom width is $2+3+6=11$, top total width $7+4=11$, so middle part is $3$ in wide, height $8$ in. The top combined: the large top rectangle is $11$ in wide, $5$ in tall, plus the top-left extension: $7$ in wide, $4$ in tall.
Correct split:

Step1: Split into 3 rectangles

1. Upper left: $7$ in $\times 4$ in
2. Upper right: $11$ in $\times 5$ in
3. Lower: $3$ in $\times 8$ in

Step2: Calculate area of upper left

$A_1 = 7 \times 4 = 28$

Step3: Calculate area of upper right

Total width: $7 + 4 = 11$ in. $A_2 = 11 \times 5 = 55$

Step4: Calculate area of lower rectangle

$A_3 = 3 \times 8 = 24$

Step5: Sum all areas

$A = A_1 + A_2 + A_3$

Answer:

$28 + 55 + 24 = 107$ square inches