Exercise 1 Page 460

First we will calculate the perimeter and the area of the original figure. Then we will use this information to calculate the perimeter and the area of the dilated figure.

Perimeter and Area of the Original Figure

Let's start with the perimeter P of the given trapezoid. To calculate it, we will add the lengths of all the sides of the trapezoid. P=3cm+6cm+5cm+2cm=16cmThe perimeter of the given trapezoid is 16cm. Next we will calculate its area. Let's recall the formula for the area of a trapezoid. A=1/2h(b_1+b_2) Here b_1 and b_2 represent the lengths of the trapezoid's bases and h is the distance between the bases. In our case b_1= 2, b_2= 6, and h= 3.

The area of the given trapezoid is 12cm^2.

Perimeter and Area of Dilated Figure

Recall that if a figure is dilated by a scale factor k then its perimeter is k times the perimeter of the original figure. In our case the perimeter of the original trapezoid is P=16cm. cc Scale factor, k & Perimeter, kP [1em] 2 & 2(16cm)=32cm Now recall that if a figure is dilated by a scale factor k then its area is k^2 times the area of the original figure. In our case the area of the original trapezoid is A=12cm^2. cc Scale factor, k & Area,k^2A [1em] 2 & ( 2^2)(12cm^2)=48cm^2

Now we can perform the same calculations using the scale factor 3. Let's start with the perimeter. cc Scale factor, k & Perimeter, kP [1em] 3 & 3(16cm)=48cm Next we can find the area. cc Scale factor, k & Area,k^2A [1em] 3 & ( 3^2)(12cm^2)=108cm^2

Finally, we will find the dilated perimeter and area using a scale factor of 4. ccc Scale factor, k & Perimeter, kP & Area,k^2A [1em] 4 & 4(16cm)=64cm & ( 4^2)(12cm^2)=192cm^2