Cogito
Grade 6 Math · Chapter 7 · Lesson 3
Area of a Parallelogram
Cut a piece off one end and slide it to the other.
10 problems · about 18 minutes · 6.G.A.1
What this lesson teaches
The child finds the area of a parallelogram and uses the perpendicular height rather than a slanted side.
- A parallelogram rearranges into a rectangle with the same area.
- Area = base × height.
- The height is the perpendicular distance, never the slanted side.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Surface Area from Nets: A cube with edge 5. Surface area?
Answer 150
Why 150.
Review — Area of Triangles: Base 14, height 6. Area?
Answer 42
Why 42.
Review — Two Variables That Move Together: If y = 5x, what is y when x is 8?
Answer 40
Why 40.
Warm Up
Straightforward practice. Get the method working first.
3 problemsBase 8, height 7. Area?
Answer 56
Why 56 square units.
Base 5, height 3. Area?
Answer 15
Why 5 × 3.
Base 12, height 4. Area?
Answer 48
Why 12 × 4.
Build It Up
The same ideas with more to keep track of.
2 problemsArea 24 and base 6. What is the height?
Answer 4
Why 24 ÷ 6.
Should the slanted side be used in the area formula?
Answer No. Use the straight-up height.
Why The rearranged rectangle has the height as a side.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Flag: A parallelogram has base 7 and height 6. What is its area?
Answer 42
Why 42 square units.
The Extra Number: Base 9, height 4, slanted side 5. What is the area?
Answer 36
Why 9 × 4 = 36.