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

1 answer

To find the area of the triangular sail, we first need to calculate the area of the triangle in George's 1/25 scale drawing, and then scale it up to the actual sail size.

The formula for the area of a triangle is:

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

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

\[ \text{Area} = \frac{1}{2} \times 1 , \text{ft} \times 2 , \text{ft} = \frac{1}{2} \times 2 = 1 , \text{square foot} \]

Now, since George's drawing is a 1/25 scale drawing, we must determine the actual dimensions of the sail. The actual dimensions will be:

  • Actual height = \(2 , \text{ft} \times 25 = 50 , \text{ft}\)
  • Actual base = \(1 , \text{ft} \times 25 = 25 , \text{ft}\)

Now, we use the area formula again for the actual sail dimensions:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 25 , \text{ft} \times 50 , \text{ft} \]

Calculating that:

\[ \text{Area} = \frac{1}{2} \times 25 \times 50 = \frac{1}{2} \times 1250 = 625 , \text{square feet} \]

Therefore, the area of the actual sail is:

\[ \boxed{625} , \text{square feet} \]