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

6.4 square inches
6.4 square inches

3.2 square inches
3.2 square inches

1.6 square inches

1 answer

To calculate the area of the triangle, we first need to find 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:

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

Now, we will determine the scale factor from the original triangle to the scale drawing. The original height is 5 inches, and the height of the scale drawing is 2 inches.

The scale factor is:

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

Since area changes with the square of the scale factor, we find the area of the scale drawing using:

\[ \text{Area of scale drawing} = \text{Area of original triangle} \times \left(\text{Scale factor}\right)^2 \]

Calculating the area of the scale drawing:

\[ \text{Area of scale drawing} = 20 \times \left(\frac{2}{5}\right)^2 = 20 \times \frac{4}{25} = \frac{80}{25} = 3.2 \text{ square inches} \]

The area of Crystal's scale drawing is \( \boxed{3.2} \) square inches.