Question

A 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) in easy wrriting

Answer 1

To find the area of Magnolia's scale drawing of the triangular flag, we first need to use the area formula for a triangle, which is:

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

Step 1: Calculate the area of the actual flag

The actual flag has a height of 15 inches and a base length of 25 inches. Plugging these values into the area formula:

$$\text{Area}=\frac{1}{2}\times 25,\text{inches}\times 15,\text{inches}$$

Calculating that step by step:

1. First, multiply the base and the height: $$25\times 15=375,\text{square inches}$$

2. Now, multiply by $\frac{1}{2}$: $$\frac{1}{2}\times 375=187.5,\text{square inches}$$

So, the area of the actual flag is 187.5 square inches.

Step 2: Calculate the area of Magnolia's scale drawing

Magnolia's scale drawing has a base of 10 inches. To find the height of the scale drawing, we need to maintain the same ratio as the actual flag.

The ratio of the base lengths is: $$\text{Scale ratio}=\frac{\text{Base of scale drawing}}{\text{Base of actual flag}}=\frac{10}{25}=\frac{2}{5}$$

Since both height and base are proportional, the height of the scale drawing will also follow this ratio.

Calculating the height of the scale drawing: $$\text{Height of scale drawing}=\text{Height of actual flag}\times \text{Scale ratio}=15\times \frac{2}{5}=6,\text{inches}$$

Step 3: Calculate the area of the scale drawing

Now we use the height of the scale drawing (6 inches) and the base length (10 inches) in the area formula:

$$\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 10,\text{inches}\times 6,\text{inches}$$

1. Multiply the base and the height: $$10\times 6=60,\text{square inches}$$

2. Now, multiply by $\frac{1}{2}$: $$\frac{1}{2}\times 60=30,\text{square inches}$$

Conclusion

The area of Magnolia’s scale drawing is 30 square inches.