Scale Drawings and Area Relationships

Mrs. Apia's lesson 15 focuses on solving area problems using scale drawings. Students learn to calculate the area of scale drawings using scale factors and percentages. The lesson includes examples with squares, circles, and rectangles, demonstrating how to determine scale factors and their impact on area. Key concepts include the relationship between scale factors and area, and how to express these relationships in fractions, decimals, and percentages.

What is the primary student outcome for this lesson on scale drawings?

• To memorize formulas for area calculations.

• To understand the history of scale drawings.

• To learn how to draw scale drawings accurately.

• To solve area problems using scale drawings and percentages.

How do you determine the area of a scale drawing if you know the scale factor and the area of the original drawing?

• Add the scale factor to the area of the original.

• Multiply the area of the original by the scale factor.

• Divide the area of the original by the scale factor.

• Multiply the area of the original by the square of the scale factor.

In the example with side lengths of 3 and 9, what is the scale factor?

• 1

• 2

• 4

• 3

What is the area of a square with a side length of 9 units?

• 36 square units

• 27 square units

• 81 square units

• 18 square units

If the radius of a circle in a scale drawing is twice that of the original, what is the scale factor for the area?

• 16

• 8

• 4

• 2

What happens to the area of a shape if the scale factor of its side lengths is 0.5?

• The area is quartered.

• The area is doubled.

• The area remains the same.

• The area is halved.

How is the quotient of the areas related to the scale factor?

• It is the scale factor cubed.

• It is the scale factor halved.

• It is the scale factor doubled.

• It is the scale factor squared.

Why is the scale factor often expressed as a percent?

• To determine if the drawing is an enlargement or reduction.

• To make calculations easier.

• To simplify the drawing process.

• To avoid using fractions.

What is the shortcut method for finding the area of a scale drawing?

• Add the scale factor to the original area.

• Divide the original area by the scale factor.

• Square the scale factor and convert it to a percent.

• Multiply the original area by the scale factor.

If the scale factor is known, is it necessary to find the area of each drawing to determine the ratio of areas?

• Yes, always.

• No, the scale factor cubed gives the ratio.

• No, the scale factor squared gives the ratio.

• Yes, but only for circles.