Question

practice 2
a trapezoid has an area of 100 square units. what scale factor would be required to dilate the trapezoid to have each area?
a. 6400 square units
type your answers in the boxes.
b. 900 square units
c. 100 square units
1
d. 25 square units
e. 4 square units
how did i do? try again

Explanation:

Part a:

Step1: Recall area scale factor formula

When a figure is dilated by a scale factor \( k \), the area of the dilated figure is \( k^2 \) times the area of the original figure. Let the original area be \( A_0 = 100 \) and the new area be \( A = 6400 \). We need to find \( k \) such that \( A=k^{2}A_{0} \).

Step2: Solve for \( k \)

First, rewrite the formula as \( k^{2}=\frac{A}{A_{0}} \). Substitute \( A = 6400 \) and \( A_0=100 \) into the formula: \( k^{2}=\frac{6400}{100}=64 \). Then take the square root of both sides: \( k = \sqrt{64}=8 \) (we take the positive square root since scale factor is positive).

Step1: Use area scale factor formula

Let \( A_0 = 100 \) and \( A = 900 \). We use \( k^{2}=\frac{A}{A_{0}} \).

Step2: Calculate \( k \)

Substitute the values: \( k^{2}=\frac{900}{100} = 9 \). Take the square root: \( k=\sqrt{9}=3 \).

Step1: Apply area scale factor formula

Let \( A_0 = 100 \) and \( A = 100 \). Use \( k^{2}=\frac{A}{A_{0}} \).

Step2: Find \( k \)

Substitute the values: \( k^{2}=\frac{100}{100}=1 \). Take the square root: \( k = \sqrt{1}=1 \).

Answer:

8

Part b: