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

20 square inches
20 square inches

1.6 square inches
1.6 square inches

6.4 square inches
6.4 square inches

3.2 square inches

Answer 1

To find the area of a triangle, we use the formula:

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

For Crystal's piece of wood, the base is 8 inches and the height is 5 inches. Therefore, the area of the original triangle would be:

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

Next, we need to calculate the area of the scale drawing. The scale drawing has a height of 2 inches, which is \( \frac{2}{5} \) of the original height (5 inches). The base of the scale drawing will be scaled down in the same ratio.

The scale factor is:

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

Since the base of the original triangle is 8 inches, the base of the scale drawing will be:

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

Now we can find the area of the scale drawing using the triangle area formula:

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

Substituting the values:

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

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