Question

Deion dilates this composite figure using a scale factor of 1/2. Determine the area of the dilated figure in square units.
The image shows a trapezoid with sides 4, 3, 6. 4 and 6 are the base and 3 is the height.

0.75 square units
3.75 square units
3 square units
15 square units

Answer 1

To find the area of the dilated figure, we first need to calculate the area of the original trapezoid.

The formula for the area \( A \) of a trapezoid is given by:

\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]

where \( b_1 \) and \( b_2 \) are the lengths of the two bases and \( h \) is the height. In this case, the bases are 4 and 6, and the height is 3.

Plugging in the values:

\[
A = \frac{1}{2} \times (4 + 6) \times 3
\]
\[
A = \frac{1}{2} \times 10 \times 3
\]
\[
A = \frac{30}{2} = 15 \text{ square units}
\]

Now, since Deion dilates the trapezoid using a scale factor of \( \frac{1}{2} \), the area of a shape dilated by a scale factor \( k \) is affected by \( k^2 \).

In this case, the scale factor is \( \frac{1}{2} \), so:

\[
k^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}
\]

Now we multiply the original area by \( \frac{1}{4} \):

\[
\text{Area of the dilated figure} = 15 \times \frac{1}{4} = \frac{15}{4} = 3.75 \text{ square units}
\]

Thus, the area of the dilated figure is \( \boxed{3.75} \) square units.