Question

A trapezoid has base lengths 4 in. and 8 in. and height 8 in. What happens to the area and the perimeter of the trapezoid when its bases and height are all multiplied by 1/8 (one-eighth)?

The perimeter is multiplied by 1/4. The area is multiplied by 1/8.

The perimeter is multiplied by 1/4. The area is multiplied by 1/16.

The perimeter is multiplied by 1/64. The area is multiplied by 1/64.

The perimeter is multiplied by 1/8. The area is multiplied by 1/64.

Answer 1

lol

Answer 2

Are you able to help me?

Answer 3

This is a question about similarity. Similar figures are simply scaled up or down copies of the original figure.

Here the new figure has a scale factor of 1/8 (since each new side is exactly 1/8 of the old)
Therefore the perimeter must also be 1/8 of the original.

The area though would be (1/8)^2 of the original = 1/64 because area is two dimensions, so multiplying 1/8 by 1/8 gives 1/64 for the two dimensions used.

In general if a figure is a scale factor of a:b of the original:
Then each side (and the perimeter) is a factor a:b of the original sides
The area scale factor is the square of this so a^2:b^2
\[Area_{new} = (a^2:b^2) Area_{old}\]
Volume would be the cube of this so a^3:b^3.

You can also test this by seeing your actual sides
Here you have

Answer 4

can you explain what \((a^2:b^2)\) is

Answer 5

Yes what is that formula? and the answer would be -> The perimeter is multiplied by 1/8. The area is multiplied by 1/64

Answer 6

a:b is the scale factor between the new and old figures. so in this case it is 1:8
(a:b)^2 is then the square of this which is 1:64

Answer 7

As an example: