Question

The area of the Real Object is equal to the area of the scale drawing divided by the square of the scale factor

12 on the bottom and top of the rectangle
4 on the right and left side of the rectangle

1:2 is an example of a scale factor written as a ratio. What is the scale factor written as a fraction?

A 1/2
B 2/1
C 2:1
D 1:2

Square of scale factor 1/2 is:

Option 1 4/1
Option 2 4:1
Option 3 1/4

Divide the scale drawing area by the square of the scale factor to find the area of the Real Object

Area of Real Object: 48 ÷ 1/4 = *blank* square units

Answer 1

Let's break this down step by step based on your information.

1. **Scale Factor written as a fraction:**
The scale factor of 1:2 can be expressed as a fraction.
- **Scale factor as a fraction:**
A scale factor of 1:2 can be written as **1/2**.
- Therefore, the correct answer is: **A 1/2**

2. **Square of the scale factor:**
To find the square of the scale factor **(1/2)**:
\[
\left( \frac{1}{2} \right)^2 = \frac{1}{4}
\]
- So, the square of the scale factor is **1/4**.
- Therefore, the correct answer is: **Option 3 1/4**

3. **Finding the area of the Real Object:**
You provided the area of the scale drawing as 48 square units. To find the area of the Real Object using the formula:

\[
\text{Area of Real Object} = \frac{\text{Area of scale drawing}}{\text{Square of scale factor}}
\]

Substitute the values:

\[
\text{Area of Real Object} = \frac{48}{1/4}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{48}{1/4} = 48 \times 4 = 192
\]

So, the area of the Real Object is **192 square units**.

**Summary of Answers:**
1. Scale factor (as a fraction): **A 1/2**
2. Square of scale factor: **Option 3 1/4**
3. Area of Real Object: **192 square units**.