Question

A triangular flag has a base length of 21 inches and a height of 49 inches. Dillon makes a scale drawing of the flag in which the height is 14 inches. Dillon needs to find the area of the drawing.

Find the area of the scale drawing.
*
2 points
Your answer

Answer 1

To find the area of the triangular flag and then determine the area of the scale drawing, we can use the formula for the area of a triangle:

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

First, we calculate the area of the actual flag:

- Base length = 21 inches
- Height = 49 inches

\[
\text{Area} = \frac{1}{2} \times 21 \times 49
\]

Calculating this:

\[
\text{Area} = \frac{1}{2} \times 21 \times 49 = \frac{1}{2} \times 1029 = 514.5 \text{ square inches}
\]

Next, we consider the scale drawing. Dillon reduces the height of the flag to 14 inches. To determine the scale factor, we compare the height of the drawing to the original height:

\[
\text{Scale factor} = \frac{\text{height of drawing}}{\text{original height}} = \frac{14}{49} = \frac{2}{7}
\]

Next, we apply this scale factor to the base length:

\[
\text{Base of drawing} = \text{original base} \times \text{scale factor} = 21 \times \frac{2}{7} = 6 \text{ inches}
\]

Now, we can find the area of the scale drawing using the base of the scale drawing and its height:

- Base of drawing = 6 inches
- Height of drawing = 14 inches

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

Calculating this:

\[
\text{Area of scale drawing} = \frac{1}{2} \times 6 \times 14 = 3 \times 14 = 42 \text{ square inches}
\]

Thus, the area of the scale drawing is:

\[
\boxed{42} \text{ square inches}
\]