SME
Grade 3 Math · Problem type
Area and the distributive property
Use this to split a rectangle into two and add the areas: 6 × 8 = 6 × 5 + 6 × 3.
Diagram
6 × 8 = 6 × 5 + 6 × 3 = 30 + 18
= 48
This is an example. Type your own values to start a new problem.
Width
×
Length
=
Width
×
First length
+
Width
×
Second length
=
First area
+
Second area
=
Area
Formulas
5 + 3 = 8
First length + second length = length
6 × 5 = 30
Width × first length = first area
6 × 3 = 18
Width × second length = second area
30 + 18 = 48
First area + second area = area
6 × 8 = 48
Width × length = area
Assumptions
•
Cut the rectangle into two rectangles. The area is the two areas added.
•
So 6 × 8 = 6 × 5 + 6 × 3: use facts you know.
Step-by-step
WE KNOW
Second length: 3 cm
Width: 6 cm
First length: 5 cm
FIND
length, first area, second area, area
Step 1 · Find length
5 + 3 = ?
First length + second length = length
Add the first length and the second length.
Length = 8 cm
Step 2 · Find first area
6 × 5 = ?
Width × first length = first area
Multiply the width by the first length.
5 × 5 = 25
One more group: 25 + 5 = 30
First area = 30 cm²
Step 3 · Find second area
6 × 3 = ?
Width × second length = second area
Multiply the width by the second length.
5 × 3 = 15
One more group: 15 + 3 = 18
Second area = 18 cm²
Step 4 · Find area
30 + 18 = ?
First area + second area = area
Add the first area and the second area.
30 + 10 = 40
40 + 8 = 48
Area = 48 cm²
Check
Put the numbers back in. Both sides should match.
5 + 3 = 8 ✓
6 × 5 = 30 ✓
6 × 3 = 18 ✓
30 + 18 = 48 ✓
6 × 8 = 48 ✓
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 of composite figures
Use this to find the area of an L-shape made of two rectangles.
Area of a shape with a corner cut out
Use this for an L-shape: the whole rectangle take away the corner cut out.