Question

vince created a scale drawing of a dog pen he wants to build as shown in the diagram.

based on the scale drawing, determine the area of the actual dog pen that vince is going to build:

hint: use the formula sheet to determine the formula(s) needed to solve the problem.

a. (135\text{ ft}^2)
b. (45\text{ ft}^2)
c. (30\text{ ft}^2)
d. (15\text{ ft}^2)

Explanation:

🆕 New Concept Discovered: Scale Drawings and Area
Converting scale dimensions to actual dimensions before calculating area.

Step 1: Find the scale dimensions of the drawing

By counting the tick marks on the scale drawing:

• The top side (length) has \( 5 \) units/inches.
• The left side (width) has \( 3 \) units/inches.

So, the dimensions on the drawing are:

• \(\text{Length} = 5\text{ inches}\)
• \(\text{Width} = 3\text{ inches}\)

Step 2: Convert drawing dimensions to actual dimensions

The scale is given as:

$$ \frac{1\text{ in}}{3\text{ ft}} $$

This means every \( 1\text{ inch} \) on the drawing represents \( 3\text{ feet} \) in real life.

• \(\text{Actual Length} = 5\text{ in} \times 3\text{ ft/in} = 15\text{ ft}\)
• \(\text{Actual Width} = 3\text{ in} \times 3\text{ ft/in} = 9\text{ ft}\)

Step 3: Calculate the actual area

Using the area formula for a rectangle:

$$ \text{Area} = \text{length} \times \text{width} $$

$$ \text{Area} = 15\text{ ft} \times 9\text{ ft} = 135\text{ ft}^2 $$

Answer:

A (135 \(\text{ft}^2\))