Question

A toy ship has a sail with measures in the diagram below. If a drawing is made of the sail with a 0.75 inch height. What will the area of the drawing of the sail be?
*
1 point
3 inches tall 8 inches wide
0.75 square inches
2 square inches
1 square inch
1.5 square inches

Answer 1

To find the area of the sail in the drawing, we first need to determine the original dimensions and then scale them down to the new height of 0.75 inches.

The original sail is 3 inches tall and 8 inches wide. The area of a rectangle is calculated as:

\[
\text{Area} = \text{height} \times \text{width}
\]

So the original area is:

\[
\text{Area}_{\text{original}} = 3 \text{ inches} \times 8 \text{ inches} = 24 \text{ square inches}
\]

Next, we need to determine the scale factor based on the height of the drawing compared to the original height:

\[
\text{Scale factor} = \frac{\text{height of drawing}}{\text{original height}} = \frac{0.75 \text{ inches}}{3 \text{ inches}} = \frac{1}{4}
\]

We apply this scale factor to both dimensions of the sail (height and width) to find the dimensions of the drawing.

The new width can be calculated as:

\[
\text{New width} = 8 \text{ inches} \times \frac{1}{4} = 2 \text{ inches}
\]

Now we can calculate the area of the drawing using the new dimensions:

\[
\text{Area}_{\text{drawing}} = \text{height}_{\text{drawing}} \times \text{width}_{\text{drawing}} = 0.75 \text{ inches} \times 2 \text{ inches} = 1.5 \text{ square inches}
\]

Therefore, the area of the drawing of the sail is:

**1.5 square inches**.