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Cogito

Grade 6 Math · Chapter 7 · Lesson 5

Practice Worksheet

Breaking a Shape Apart

An awkward outline is a few easy ones.

10 problems · about 19 minutes · 6.G.A.1

NameDate

Figure — use these to answer the problems

One piece of the shape at a time. Add the pieces at the end.

Area · squares inside

18

Perimeter · walk around

18

6 × 3 = 18 · 6 + 3 + 6 + 3 = 18

Width of this piece6
Height of this piece3
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

3 problems

  1. From “Area of a Trapezoid”

    Parallel sides 5 and 11, height 4. Area?

    Answer

  2. From “Area of a Parallelogram”

    Base 8, height 7. Area?

    Answer

  3. From “Surface Area from Nets”

    A cube with edge 5. Surface area?

    Answer

Warm Up

Straightforward practice. Get the method working first.

3 problems

  1. A 7 by 4 rectangle with a 3 by 2 piece removed. Area left?

    Answer

  2. Pieces of 3 by 3 and 4 by 2. Total area?

    Answer

  3. A 6 by 6 square with a 2 by 2 corner removed. Area left?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Pieces of 5 by 4 and a triangle of base 4, height 3. Total area?

    Answer

  2. Must the pieces overlap to cover the shape?

    • No. Overlaps would be counted twice.
    • Yes.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. Two Rectangles

    One piece is 4 by 3, the other 5 by 2. What is the total area?

    Answer

  2. The Bite

    A 10 by 5 rectangle with a 4 by 2 piece removed. What area is left?

    Answer