Dimensional Change

What formula should you use to find the new perimeter of a figure after dilation?

• (scale factor) + (original perimeter)

• (original perimeter) x (new perimeter)

• (scale factor) x (perimeter)

• (scale factor) x (scale factor) x (perimeter)

Answer explanation

When given the perimeter of a shape and a scale factor. You can find the perimeter of the new shape by multiplying the original perimeter by the scale factor.

Which formula should you use to find the new area of a figure after dilation?

• (original area) + (original area) + (scale factor)

• (scale factor) x (original area)

• (scale factor) + (scale factor) + (area)

• (scale factor) x (scale factor) x (area)

Answer explanation

When given the area of a figure and the scale factor, you can calculate the area of the new figure by squaring the scale factor and multiplying it by the original area.

Original Area × (Scale Factor)² = New Area

Rectangle ABCD is similar to Rectangle A'B'C'D'. Each dimension of A'B'C'D' is 3 times that of ABCD. Which statement is true?

• The area of A'B'C'D' is 6 times the area of ABCD.

• The perimeter of A'B'C'D' is 6 times the perimeter of ABCD.

• The area of A'B'C'D' is 9 times the area of ABCD.

• The perimeter of A'B'C'D' is 9 times the perimeter of ABCD.

Answer explanation

When given the area of a figure and the scale factor, you can calculate the area of the new figure by squaring the scale factor and multiplying it by the original area.

Original Area × (Scale Factor)² = New Area

Square WXYZ is similar to Square W'X'Y'Z'. Each dimension of Square W'X'Y'Z' is .5 times that of Square WXYZ. What is true?

• The area of Square W'X'Y'Z' is .5 times the area of Square WXYZ.

• The perimeter of Square W'X'Y'Z' is .5 times the perimeter of Square WXYZ.

• The area of Square W'X'Y'Z' is 1 times the area of Square WXYZ.

• The perimeter of Square W'X'Y'Z' is .25 times the perimeter of Square WXYZ.

Answer explanation

When given the perimeter of a shape and a scale factor. You can find the perimeter of the new shape by multiplying the original perimeter by the scale factor.

Square A is similar to Square B. Each dimension of Square B is 2.5 times the dimension of Square A. Which statement is true?

• The area of Square B is 6.25 times the area of Square A.

• The perimeter of Square B is 6.25 times the perimeter of Square A.

• The area of Square B is 2.5 times the area of Square A.

• The perimeter of Square B is 5 times the perimeter of Square A.

Answer explanation

When given the area of a figure and the scale factor, you can calculate the area of the new figure by squaring the scale factor and multiplying it by the original area.

Original Area × (Scale Factor)² = New Area

Rectangle GHJK is similar to Rectangle G'H'J'K'. Each dimension of G'H'J'K' is 1/4 of GHJK. Which statement is true?

• The perimeter of G'H'J'K' is 1/4 of GHJK's perimeter.

• The perimeter of G'H'J'K' is 1/16 of GHJK's perimeter.

• The area of G'H'J'K' is 1/2 of GHJK's area.

• The area of G'H'J'K' is 1/2 of GHJK's area.

Answer explanation

When given the perimeter of a shape and a scale factor. You can find the perimeter of the new shape by multiplying the original perimeter by the scale factor.

A quadrilateral is dilated by a factor of 2. If its original perimeter is x units, what is the new perimeter?

• 2²x units

• 0.5x units

• 2x units

• x units

Answer explanation

When given the perimeter of a shape and a scale factor. You can find the perimeter of the new shape by multiplying the original perimeter by the scale factor.

Franklin draws a rectangle with an area of 12 in². The rectangle is dilated by a scale factor of 1/2. What is the new area?

• 3 in²

• 4 in²

• 6 in²

• 24 in²

Answer explanation

When given the area of a figure and the scale factor, you can calculate the area of the new figure by squaring the scale factor and multiplying it by the original area.

Original Area × (Scale Factor)² = New Area

A pentagon has sides of 7 inches. It is doubled in size. What is the new perimeter?

• 14 inches

• 35 inches

• 70 inches

• 140 inches

Answer explanation

When given the perimeter of a shape and a scale factor. You can find the perimeter of the new shape by multiplying the original perimeter by the scale factor.

A triangle's perimeter is 20 cm. It is dilated by a scale factor of 4/5. What is the new perimeter?

• 16 cm

• 25 cm

• 48 cm

• 75 cm

Answer explanation

When given the perimeter of a shape and a scale factor. You can find the perimeter of the new shape by multiplying the original perimeter by the scale factor.