Question

Sinclair applied a dimensional change to a trapezoid with a height of 5 and base lengths 3 and 7 to determine the effect a proportional change has on the area. His work is shown below. 1. Original: A = 1 2 (3+7)(5) = 25 ft2 2. New: A = 1 2 ( 1 + 7 3 ) ( 5 3 ) = 25 9 ft2 3. Compare volumes: 25 9 25 = 25 9 ( 1 25 ) = 1 9 Use Sinclair’s work to answer the questions and complete the statements. How did Sinclair come up with the dimensions 1, 7 3 , and 5 3 in step 2? He multiplied the original dimensions by a scale factor of . What can Sinclair conclude about the effect on the trapezoid’s area from his comparison? The changes created an area times the original area.

Answer 1

Sinclair applied a dimensional change to a trapezoid with a height of 5 and base lengths 3 and 7 to determine the effect a proportional change has on the area. His work is shown below.

1. Original: A =

1

2

(3+7)(5) = 25 ft2

2. New: A =

1

2

( 1 +

7

3

) (

5

3

) =

25

9

ft2

3. Compare volumes:

25

9

25

=

25

9

(

1

25

) =

1

9

Use Sinclair’s work to answer the questions and complete the statements.

How did Sinclair come up with the dimensions 1,

7

3

, and

5

3

in step 2?

He multiplied the original dimensions by a scale factor of

✔ 1/3

.

What can Sinclair conclude about the effect on the trapezoid’s area from his comparison?

The changes created an area

✔ 1/9

times the original area.

Explanation:

Answer 2

Late but it was

1/3

1/9