No formula exists for an L-shape. Cut it into two rectangles and add their areas.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Finding the lengths you were not given
A cut usually creates a side with no number on it. Work it out by subtracting from the full side.
Sometimes take away instead
A rectangle with a bite out of it is easier as the whole rectangle minus the bite.
Check the pieces fit
The pieces must cover the shape exactly, with no gaps and no overlaps.
Split into shapes you can handle
An awkward outline can almost always be cut into rectangles and triangles. Find each piece's area and add. The only judgement needed is where to cut, and any cut that produces shapes you know how to measure will do.
Or subtract from a bigger shape
Sometimes it is easier to enclose the shape in a rectangle and subtract the parts that are not in it. For a shape with a notch cut out, subtracting is far quicker than splitting. Try both mentally before committing.
Fill in the missing lengths first
Composite diagrams withhold measurements on purpose. If the whole top edge is 14 and one part is 9, the other is 5. Work out every length and write it on the diagram before calculating any area — most errors here are missing lengths, not arithmetic.
Check the total against a rough estimate
Judge roughly what fraction of the enclosing rectangle the shape covers, and compare with your calculated area. If the shape clearly covers most of a 100 square unit rectangle and you calculated 30, a piece went missing.
Step 2: Try It Yourself
Tap and try it out.
Area · squares inside
18
Perimeter · walk around
18
6 × 3 = 18 · 6 + 3 + 6 + 3 = 18
Area counts the squares inside. Perimeter measures the walk all the way round.
Step 3: Watch an Example
One step at a time.
Watch Ana Split an L-Shape
An L is 8 wide and 6 tall overall, with a 5 by 3 rectangle removed from the corner.
- Step 1
She works out the whole rectangle first: 8 × 6 = 48.
Step 4: Your Turn
Practice makes it stick.
Two Rectangles
Problem 1 of 2
One piece is 4 by 3, the other 5 by 2. What is the total area?
The Bite
Problem 2 of 2
A 10 by 5 rectangle with a 4 by 2 piece removed. What area is left?
Piece by Piece
1 of 4
Pieces of 3 by 3 and 4 by 2. Total area?
2 of 4
A 6 by 6 square with a 2 by 2 corner removed. Area left?
3 of 4
Pieces of 5 by 4 and a triangle of base 4, height 3. Total area?
4 of 4
Must the pieces overlap to cover the shape?
Step 5: Quick Check
Show what you know.
Question 1 of 1
A 7 by 4 rectangle with a 3 by 2 piece removed. Area left?
What You Learned
- A composite shape has no formula of its own.
- Cut it into rectangles and triangles, or subtract a missing piece from a whole.
- The pieces must fit exactly, with no gaps and no overlaps.