To find the area of Magnolia’s scale drawing of the triangular flag, we first need to determine the scale factor and then use that to compute the area.
1. **Determine the scale factor:**
The actual base length of the triangular flag is 25 inches.
The base length of the scale drawing is 10 inches.
The scale factor can be found as follows:
\[
\text{Scale Factor} = \frac{\text{Base length of scale drawing}}{\text{Base length of actual flag}} = \frac{10}{25} = \frac{2}{5}
\]
2. **Determine the corresponding height in the scale drawing:**
The height of the actual flag is 15 inches. Using the same scale factor, we calculate the height of the scale drawing:
\[
\text{Height of scale drawing} = \text{Scale Factor} \times \text{Height of actual flag} = \frac{2}{5} \times 15 = 6 \text{ inches}
\]
3. **Calculate the area of the actual triangular flag:**
The area of a triangle is given by the formula:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Applying this formula to the actual flag:
\[
\text{Area of actual flag} = \frac{1}{2} \times 25 \times 15 = \frac{1}{2} \times 375 = 187.5 \text{ square inches}
\]
4. **Calculate the area of the scale drawing:**
Similarly, we use the same area formula for the triangular flag in the scale drawing:
\[
\text{Area of scale drawing} = \frac{1}{2} \times 10 \times 6 = \frac{1}{2} \times 60 = 30 \text{ square inches}
\]
Therefore, the area of Magnolia’s scale drawing of the triangular flag is \(30\) square inches.
Work shown:
- Scale Factor = \(\frac{10}{25} = \frac{2}{5}\)
- Height of scale drawing = \(\frac{2}{5} \times 15 = 6\) inches
- Area calculation for scale drawing: \(\frac{1}{2} \times 10 \times 6 = 30\) square inches
Thus, the area of Magnolia's scale drawing is \(\boxed{30}\) square inches.
Area and Perimeter Unit Test15 of 15 15 of 15 ItemsQuestionA triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia’s scale drawing? Solve the problem by computing the actual area from the scale drawing. Show your work.(4 points)BoldItalicUnderlineIncrease indentDecrease indentFormula keypadUndoRedo Math Short Answer Rubric (4 points)Points Awarded Criteria4 The answer is clear and correct.The answer shows that the student used problem-solving skills and reasoning.All work is shown or explained.3 The answer is mostly correct. The student made small errors while solving.The answer shows that the student used some problem-solving skills and reasoning.Most work is shown or explained.2 The answer is partially correct. The student made errors while solving.The answer shows that the student used some problem-solving skills or reasoning.Some work is shown or explained.1 The answer is incorrect. The student made errors while solving.The answer shows little problem-solving skills or reasoning.Little or no work is shown.0 The question is not answered.
1 answer