Sign up for FREE

Decompose 2-D Figures

Last updated over 2 years ago

8 questions

1

3.6.E

1

3.6.E

1

3.6.E

1

3.6.E

1

3.6.E

1

3.6.E

1

3.6.E

1

3.6.E

Question 1

1.

Sally and Bill both make sandwiches that are congruent (the same size) for lunch. Sally cut her sandwich vertically in half and ate one piece. Bill cut his sandwich diagonally in half and also ate one piece. Who ate more? Why?

Sally ate more because rectangles are larger than triangles.

Bill ate more because triangles are wider than rectangles.

They both ate the same amount because both sandwiches are the same size and both sandwiches were cut in half, even though the shaded parts are different shapes.

Question 2

2.

Sara made two congruent cakes for her twin daughter’s birthday party. The shaded part represents the amount eaten from both cakes. Which cake had more eaten?

The chocolate cake had more eaten, because the shaded rectangle is wider.

Both cakes had the same amount eaten because both shaded rectangles represent 1/4 of the entire cake and both cakes are the same size.

Both cakes had the same amount eaten because both shaded rectangles represent 1/2 of the entire cake and both cakes are the same size.

Question 3

3.

The figures below are congruent. Which statement about the shaded areas of these figures is true?

The shaded areas of the figures are equal, even though they do not have the same shapes, because they both represent one-half of the same whole.

The shaded areas of the figures are not equal because the figures are not the same size.

The shaded areas of the figures are not equal because they are not the same shape.

Question 4

4.

Two chefs made identical rectangular cakes. Each chef cut his cake into equal parts a different way and gave the judges 1 piece of cake.

Which chef gave the judges 1/6 of the cake?

Neither chef

Both chefs

Question 5

5.

Rashad folded two congruent trapezoids into equal areas. He shaded 2 parts of one trapezoid and 1 part of another.

Hannah said "You shaded 1/4 the area of each trapezoid." Is Hannah correct?

No, 2/8 does not represent the same area as 1/4.

No, Rashad shaded 2 parts of the first trapezoid and only 1 part of the other.

Question 6

6.

These two right triangles are congruent. Each triangle has been divided into 4 smaller right triangles of equal area.

What fraction of the whole triangle is represented by the shaded area of each triangle?

1/3

1/6

1/4

Question 7

7.

The congruent squares have each been divided into 4 equal areas. One part is shaded in each figure.

Which statement about the shaded areas is NOT true?

Each shaded area represents the fraction 1/4.

The shaded areas of the two squares are equal.

Question 8

8.

Johnna and Leo each divided a congruent parallelogram into 6 parts with equal areas. They shaded one of the 6 parts.

If the parallelograms are congruent, which statement is true?

Johnna's figure does not show 1/6 shaded, but Leo's does.

Each person shaded 1/6 of the area of their parallelogram.

There is not enough information to determine who ate more.

The vanilla cake had more eaten, because the shaded rectangle is taller.

The shaded areas of the figures are equal, even though they do not have the same shape, because they both represent one-fourth of the same size whole.

Chef Lang

Chef Bourge

Yes, 2/8 of the first trapezoid is equal in area to 1/4 of the second trapezoid.

No, the first trapezoid is larger than the second trapezoid.

1/2

The shaded part of the first square covers a greater area than the shaded part of the second square.

The shaded parts of the two squares are not the same shape.

Leo's figure does not show 1/6 shaded, but Johnna's does.

Each section in Johnna's figure is larger than each section in Leo's figure