SME
Grade 3 Math · Problem type
Area of a shape with a corner cut out
Use this for an L-shape: the whole rectangle take away the corner cut out.
Diagram
30 − 6 = 24 cm²
Width left: 4 cm
Height left: 2 cm
This is an example. Type your own values to start a new problem.
Whole width
×
Whole height
−
Cut-out width
×
Cut-out height
=
Area of the shape (cm²)
Width left
worked out (not typed)
Height left
worked out (not typed)
Formulas
6 × 5 − 2 × 3 = 24
Whole area − cut-out area = area of the shape
2 + 4 = 6
Cut-out width + width left = whole width
3 + 2 = 5
Cut-out height + height left = whole height
Assumptions
•
Find the area of the whole rectangle.
•
Take away the area of the corner that is cut out.
Step-by-step
WE KNOW
Whole width: 6 cm
Whole height: 5 cm
Cut-out width: 2 cm
Cut-out height: 3 cm
FIND
area of the shape, width left, height left
Step 1 · Find area of the shape
6 × 5 − 2 × 3 = ?
Whole area − cut-out area = area of the shape
Find the whole area and the cut-out area. Take the cut-out away.
Whole area: 6 × 5 = 30
Cut-out area: 2 × 3 = 6
30 − 6 = 24
Area of the shape = 24 cm²
Step 2 · Find width left
2 + ? = 6
Cut-out width + width left = whole width
Take the cut-out width away from the whole width.
Width left = 6 − 2
Width left = 4 cm
Step 3 · Find height left
3 + ? = 5
Cut-out height + height left = whole height
Take the cut-out height away from the whole height.
Height left = 5 − 3
Height left = 2 cm
Check
Put the numbers back in. Both sides should match.
6 × 5 − 2 × 3 = 24 ✓
2 + 4 = 6 ✓
3 + 2 = 5 ✓
Topic check
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Related lessons
Area and multiplication
Main lesson
Find an unknown side from the area
Use this when you know the area and one side: “24 cm², 6 cm long. How wide?”
Area and the distributive property
Use this to split a rectangle into two and add the areas: 6 × 8 = 6 × 5 + 6 × 3.
Area of composite figures
Use this to find the area of an L-shape made of two rectangles.