The rectangle’s top has 3m. The rectangles left side has 4m.

The rectangle shows the outline of a campsite in a national forest. Anna makes a scale drawing of the campsite in which the longer side measures 1 meter. What is the area of the scale drawing in square meters?

(1 point)
Responses

12 square meters
12 square meters

1.33 square meters
1.33 square meters

0.75 square meters
0.75 square meters

3.5 square centimeters

1 answer

To find the area of the scale drawing, we first need to determine the area of the original rectangle (campsite) based on its dimensions.

The original dimensions of the rectangle are:

  • Length = 4 meters (longer side)
  • Width = 3 meters (shorter side)

The area \(A\) of the rectangle can be calculated using the formula: \[ A = \text{Length} \times \text{Width} = 4 , \text{m} \times 3 , \text{m} = 12 , \text{m}^2 \]

Now, Anna makes a scale drawing such that the longer side (4 m) is represented as 1 meter in the drawing. To find the scale factor, we divide the length of the drawing by the original length: \[ \text{Scale Factor} = \frac{1 , \text{m}}{4 , \text{m}} = \frac{1}{4} \]

The shorter side (3 m) in the drawing can be calculated using the scale factor. Let's find the length of the shorter side in the scale drawing: \[ \text{Shorter Side Length in Drawing} = 3 , \text{m} \times \frac{1}{4} = 0.75 , \text{m} \]

Now we can calculate the area of the scale drawing using its dimensions: \[ \text{Area of Scale Drawing} = \text{Length} \times \text{Width} = 1 , \text{m} \times 0.75 , \text{m} = 0.75 , \text{m}^2 \]

Thus, the area of the scale drawing is \(0.75\) square meters.

The correct response is: 0.75 square meters