SEAGReady
MeasurementP7 level20 questions in the full course

Area of Compound ShapesSEAG Practice Questions

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

What your child needs to know

SEAGReady breaks area of compound shapes into 3 steps, taught in order so each skill builds on the last.

  1. 1

    L-Shapes with All Dimensions

    Split an L-shape into two rectangles and add their areas when all necessary dimensions are labeled

  2. 2

    Finding Missing Dimensions

    Calculate unlabeled dimensions from given measurements before finding the total area

  3. 3

    Subtraction Method

    Find compound shape area by calculating a large enclosing rectangle and subtracting the cut-out section

Try these SEAG-style questions

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.

Question 1Confidence builder

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?

  • A23 m²
  • B28 m²
  • C14 m²
  • D120 m²
Show answer and explanation

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?

Question 2Confidence builder

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?

  • A6 m
  • B14 m
  • C4 m
  • D10 m
Show answer and explanation

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.

Question 3Confidence builder

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?

  • A42 m²
  • B48 m²
  • C6 m²
  • D54 m²
Show answer and explanation

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?

Try the lesson: L-Shapes with All Dimensions

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)

Find the area of each rectangle
1

First rectangle: 4 m by 3 m

4 × 3 = 12 m²

Step 1 of 3

Prefer to read? See every step written out

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?

  1. 1

    Find the area of each rectangle

    • First rectangle: 4 m by 3 m4 × 3 = 12 m²
    • Second rectangle: 5 m by 2 m5 × 2 = 10 m²
  2. 2

    Add the two areas together

    • Total area = sum of both rectangles12 + 10 = 22 m²

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.

Mistakes to watch for

These are the misconceptions we see most often in area of compound shapes, including the ones our practice questions are specifically designed to catch.

  • Overlapping rectangles when splitting the shape
  • Using wrong dimensions for the sub-rectangles
  • Forgetting to add the partial areas together

Build these skills first

Struggling with area of compound shapes? The real gap is often in one of these earlier topics.

More measurement practice

20 questions on this topic alone

Master area of compound shapes and everything it unlocks

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.