Question

problem 4
ali and kiana buried a treasure together on their school’s field.
the field is 400 feet wide.

• ali made a map that is 8 inches wide to record its location.
• kiana made her own map using a scale of 1 inch to 20 feet.

on kiana’s map, the area of the field is 16 square inches. kiana says that the actual area of the field is 320 square feet.
is kiana correct?
yes no

Explanation:

Step1: Recall scale for area

When dealing with scale models (or maps), the scale for area is the square of the linear scale. The linear scale here is 1 inch to 20 feet, so the area scale is \((1\ inch : 20\ feet)^2=1\ square\ inch : 400\ square\ feet\).

Step2: Calculate actual area

Kiana's map has an area of 16 square inches. Using the area scale, the actual area should be \(16\times400 = 6400\) square feet.

Step3: Compare with Kiana's claim

Kiana claims the actual area is 320 square feet, but we calculated it as 6400 square feet. So Kiana is not correct.

Answer:

No