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

3.2 square inches
3.2 square inches

1.6 square inches
1.6 square inches

6.4 square inches
6.4 square inches

20 square inches
20 square inches
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1 answer

To find the area of Crystal's scale drawing of the triangle, we can use the formula for the area of a triangle:

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

First, we need to determine the scale factor between the original triangle and the scale drawing. The original triangle has a height of 5 inches and a base of 8 inches. The scale drawing has a height of 2 inches.

To find the scale factor:

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

Next, we can find the base of the scale drawing using the same scale factor:

\[ \text{Base of scale drawing} = \text{base of original triangle} \times \text{scale factor} = 8 \times \frac{2}{5} = \frac{16}{5} = 3.2 \text{ inches} \]

Now, we can calculate the area of the scale drawing:

\[ \text{Area} = \frac{1}{2} \times \text{Base of scale drawing} \times \text{Height of scale drawing} \]

Substituting in the values we found:

\[ \text{Area} = \frac{1}{2} \times 3.2 \times 2 = \frac{1}{2} \times 6.4 = 3.2 \text{ square inches} \]

Thus, the area of her scale drawing is:

3.2 square inches