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

6.4 square inches
6.4 square inches

1.6 square inches
1.6 square inches

20 square inches

1 answer

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

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

In the original triangle, the base is 8 inches and the height is 5 inches. The area of the original triangle is:

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

Now, to find the area of Crystal's scale drawing, we note that the height is reduced from 5 inches to 2 inches. This scale factor can be calculated by comparing the new height to the original height:

\[ \text{Scale Factor} = \frac{\text{new height}}{\text{original height}} = \frac{2}{5} \]

Since both the height and base of the triangle scale in the same ratio, the scale drawing also has a base that is scaled similarly. The base in the original triangle is 8 inches, so the base in the scale drawing is:

\[ \text{New base} = 8 \times \frac{2}{5} = 3.2 \text{ inches} \]

Now we can find the area of the scale drawing using the new height and new base:

\[ \text{Area of scale drawing} = \frac{1}{2} \times \text{New base} \times \text{New height} = \frac{1}{2} \times 3.2 \times 2 \]

Calculating this gives:

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

So, the area of Crystal's scale drawing is 3.2 square inches.