Question

George makes a 1/25
scale drawing of a triangular sail. The triangle in his drawing is 2 feet high with a base of 1 foot. What is the area of the sail?(1 point)

square feet

Answer 1

To find the area of the triangular sail, we first need to calculate the area of the triangle in George's drawing and then scale it up to the actual size of the sail.

The area \( A \) of a triangle can be calculated using the formula:

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

In George's drawing, the base is 1 foot and the height is 2 feet. Plugging in these values, we get:

\[
A = \frac{1}{2} \times 1 \, \text{foot} \times 2 \, \text{feet} = \frac{1}{2} \times 2 = 1 \, \text{square foot}
\]

This area (1 square foot) corresponds to the drawing, which is a 1/25 scale. To find the actual area of the sail, we need to scale the area up by the square of the scale factor (since area is a two-dimensional measurement).

The scale factor is \( 25 \), so we will multiply the area of the drawing by \( 25^2 \):

\[
\text{Actual Area} = 1 \, \text{square foot} \times 25^2 = 1 \times 625 = 625 \, \text{square feet}
\]

Thus, the area of the sail is **625 square feet**.