Finding the area of L-shapes and compound rectilinear shapes by splitting into rectangles and adding the areas.
Where your child meets this in real life: Calculating floor tiles needed for an L-shaped kitchen or grass seed for an irregular lawn
SEAGReady breaks area of compound shapes into 3 steps, taught in order so each skill builds on the last.
Split an L-shape into two rectangles and add their areas when all necessary dimensions are labeled
Calculate unlabeled dimensions from given measurements before finding the total area
Find compound shape area by calculating a large enclosing rectangle and subtracting the cut-out section
Three free sample questions from our area of compound shapes course. Every question comes with a full explanation, and hints that guide without giving the answer away.
Ciara's living room is L-shaped. It is made of two rectangular sections: one is 5 m by 3 m and the other is 4 m by 2 m. What is the total floor area?
Answer: A. 23 m²
Split the L-shape into two rectangles: First rectangle: 5 m x 3 m = 15 m² Second rectangle: 4 m x 2 m = 8 m² Total area = 15 + 8 = 23 m²
Stuck? Start here: An L-shape is made of two rectangles joined together. What do you need to find first?
An L-shaped patio is 10 m wide and 8 m tall overall. A rectangular corner is cut out that is 4 m wide and 3 m deep. What is the width of the bottom section of the L-shape?
Answer: A. 6 m
To find the missing width: Total width - cut-out width = remaining width 10 m - 4 m = 6 m
Stuck? Start here: Look at the total width and the width of the cut-out corner.
A rectangular garden is 8 m by 6 m. A rectangular shed in the corner is 3 m by 2 m. What area of garden remains for grass?
Answer: A. 42 m²
Full garden area: 8 m x 6 m = 48 m² Shed area: 3 m x 2 m = 6 m² Grass area = 48 - 6 = 42 m²
Stuck? Start here: The shed takes away some garden space. What operation removes something?
This is the exact interactive worked example your child sees in SEAGReady. Step through it and watch the method build up.
Aoife's bedroom is an L-shape. She wants to buy carpet for the floor. The room is made of two rectangular sections: one is 4 m by 3 m and the other is 5 m by 2 m.
What is the total floor area of the bedroom?
(4 × 3) + (5 × 2)
Step 1 of 3
Aoife's bedroom is an L-shape. She wants to buy carpet for the floor. The room is made of two rectangular sections: one is 4 m by 3 m and the other is 5 m by 2 m.
What is the total floor area of the bedroom?
The total floor area is 22 m².
The key insight: Split any compound shape into rectangles, find each area, then add them up!
Watch out: 4 × 3 × 5 × 2 = 120 m². Multiplying all dimensions together is incorrect - calculate each rectangle separately, then add.
These are the misconceptions we see most often in area of compound shapes, including the ones our practice questions are specifically designed to catch.
Struggling with area of compound shapes? The real gap is often in one of these earlier topics.
SEAGReady finds the exact step where your child gets stuck, teaches it with worked examples like the one above, and brings it back for review so it sticks.