To enlarge the shape by a factor of 2, we have to double all of the shape's sides.
Diagram:
Original Perimeter: 18 units Enlarged Perimeter: 36 units Perimeter Comparison: The enlarged shape has twice as long of a perimeter
Original Area: 18 units Enlarged Area: 76 units Area Comparison: The enlarged shape has four times the area
Practice makes perfect
To enlarge the shape by a factor of 2, we have to double all of the shape's sides.
4( 2)&=8
6( 2)&=12
5( 2)&=10
3( 2)&=6
Now we can draw the dilated figure.
Perimeter
To find the perimeter, we have to add all of the shape's sides.
Comparing the areas, we notice that the enlarged shape has a perimeter that's twice that of the original shape. This makes sense, as we have enlarged it by a factor of 2.
Area
Notice that this is a quadrilateral where two sides are parallel, making it a trapezoid. To calculate a trapezoid's area, we multiply its height with the sum of its parallel sides, and divide the product by 2.
By dividing the larger area by the smaller area, we get the ratio between them.
72/18=4
When enlarging the shape by a factor of 2, we quadruple the area. In fact, the area of a dilated shape is always the square of the factor of dilation.
