Cogito
Grade 6 Math · Chapter 7 · Lesson 5
Breaking a Shape Apart
An awkward outline is a few easy ones.
10 problems · about 19 minutes · 6.G.A.1
What this lesson teaches
The child finds the area of a composite figure by decomposing it into rectangles and triangles.
- 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.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Area of a Trapezoid: Parallel sides 5 and 11, height 4. Area?
Answer 32
Why 32 square units.
Review — Area of a Parallelogram: Base 8, height 7. Area?
Answer 56
Why 56 square units.
Review — Surface Area from Nets: A cube with edge 5. Surface area?
Answer 150
Why 150.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA 7 by 4 rectangle with a 3 by 2 piece removed. Area left?
Answer 22
Why 22 square units.
Pieces of 3 by 3 and 4 by 2. Total area?
Answer 17
Why 9 and 8.
A 6 by 6 square with a 2 by 2 corner removed. Area left?
Answer 32
Why 36 − 4.
Build It Up
The same ideas with more to keep track of.
2 problemsPieces of 5 by 4 and a triangle of base 4, height 3. Total area?
Answer 26
Why 20 and 6.
Must the pieces overlap to cover the shape?
Answer No. Overlaps would be counted twice.
Why Each square of the shape belongs to one piece.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsTwo Rectangles: One piece is 4 by 3, the other 5 by 2. What is the total area?
Answer 22
Why 22 square units.
The Bite: A 10 by 5 rectangle with a 4 by 2 piece removed. What area is left?
Answer 42
Why 42 square units.