Question

Question
Use the image to answer the question.
An illustration shows a triangle with a base labeled 8 inches. A line runs through the center of the triangle from the apex to the base. This perpendicular height is labeled 5 inches.

Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?

(1 point)
Responses

6.4 square inches
6.4 square inches

3.2 square inches
3.2 square inches

20 square inches
20 square inches

1.6 square inches
1.6 square inches
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Answer 1

To find the area of Crystal's scale drawing of the triangle, we first need to calculate the area of the original triangle using the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

For the original triangle:
- Base = 8 inches
- Height = 5 inches

Calculating the area:

\[
\text{Area} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \text{ square inches}
\]

Next, we need to determine the scale of the drawing. The height of the original triangle is 5 inches and the height of the scale drawing is 2 inches.

To find the scale factor, we divide the height of the scale drawing by the height of the original triangle:

\[
\text{Scale factor} = \frac{\text{Height of scale drawing}}{\text{Height of original triangle}} = \frac{2}{5}
\]

Now, we can use the square of the scale factor to find the area scaling factor since area changes with the square of the linear dimensions:

\[
\text{Area scaling factor} = \left(\frac{2}{5}\right)^2 = \frac{4}{25}
\]

Now we can calculate the area of the scale drawing:

\[
\text{Area of scale drawing} = \text{Area of original triangle} \times \text{Area scaling factor} = 20 \times \frac{4}{25}
\]

Calculating this gives:

\[
\text{Area of scale drawing} = 20 \times \frac{4}{25} = \frac{80}{25} = 3.2 \text{ square inches}
\]

Therefore, the area of Crystal's scale drawing is:

**3.2 square inches**.