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

1.6 square inches
1.6 square inches

20 square inches
20 square inches

3.2 square inches

1 answer

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

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

First, we calculate the area of the original triangle with height 5 inches and base 8 inches:

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

Next, we find the scale factor used in the scale drawing. The original height is 5 inches, and the height of the scale drawing is 2 inches. The scale factor is:

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

The area of similar figures scales with the square of the scale factor. Therefore, the area of the scale drawing is calculated as follows:

\[ \text{Area of scale drawing} = \text{Area of original triangle} \times \left(\text{Scale factor}\right)^2 = 20 , \text{square inches} \times \left(\frac{2}{5}\right)^2 \]

Calculating this step-by-step:

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

Now compute the area:

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

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

\[ \boxed{3.2 , \text{square inches}} \]