Let’s solve this step by step.
We have an L-shaped composite figure. To find its area, we can split it into two rectangles — one on top and one on the bottom (or left and right — either way works). Let’s go with splitting it vertically.
Looking at the shape:
- The total height on the left is 8 inches.
- The top part of the L has a width of 3 inches.
- The vertical drop from the top to the inner corner is 6 inches → so the bottom rectangle’s height must be 8 - 6 = 2 inches (which matches the label on the right side).
- The bottom part extends 7 inches to the right from the inner corner, plus the 3-inch top part → total bottom width is 10 inches (also labeled).
So let’s split it into two rectangles:
Rectangle 1 (top-left):
Width = 3 in
Height = 6 in
Area = 3 × 6 = 18 square inches
Rectangle 2 (bottom-full width):
Width = 10 in
Height = 2 in
Area = 10 × 2 = 20 square inches
Wait — but if we do that, we’re double-counting? No, actually, in this case, since the top rectangle is only 3 inches wide and sits above the left part of the bottom rectangle, they don’t overlap. So adding them is fine.
But let’s check another way to make sure.
Alternative split: Split horizontally.
Top rectangle: 3 in wide × 6 in tall → 18 sq in
Bottom rectangle: 10 in wide × 2 in tall → 20 sq in
Total = 18 + 20 = 38 sq in
Another way: Think of the whole big rectangle minus the missing piece.
Big rectangle would be 10 in wide × 8 in tall = 80 sq in
Missing piece is the empty space in the upper right:
Width = 10 - 3 = 7 in
Height = 6 in
Area of missing piece = 7 × 6 = 42 sq in
So area of L-shape = 80 - 42 = 38 sq in
Same answer! Good.
Let me verify dimensions again:
Left side: 8 in total
Top segment: 3 in wide
Vertical drop inside: 6 in → so bottom part height = 8 - 6 = 2 in ✔️
Bottom extends 7 in to the right from the inner corner → so total bottom width = 3 + 7 = 10 in ✔️
Right side height: 2 in ✔️
All labels match.
So both methods give 38 square inches.
Final Answer:
38
Parent Tip: Review the logic above to help your child master the concept of area of composite figures worksheet 6th grade.
