Scale Drawings Area & Perimeter

Scale Drawings: Area & Perimeter

Recall Area and Perimeter

The area of a polygon measures the amount of space it covers.

The perimeter of a polygon measures the outer band of the polygon.

Multiple Select

Which of the following are true for a rectangle?

• A = 0.5*b*h

• P = L + W + L + W

• A = l*w

• P = 3*L

Multiple Select

Which of the following are true for a triangle?

• A = 0.5*b*h

• P = L + L + W + W

• P = sum of the 3 sides

• A = l*h

Scale Factor

Scale factor is the ratio by which a polygon changes size.

Scale factor is used as a constant of proportionality after converting it to a unit rate, so we can use the equation, y = kx.

We modify this as actual, a, equals k, scale factor, times the drawing, d or a = kd.

Multiple Choice

If a drawing has a scale of 3 cm to 9 feet, what is the scale factor (from drawing to actual)?

• -3

• -1/3

• 1/3

• 3

If a drawing has a scale of 3 cm to 9 feet, what is the scale factor (from drawing to actual)?

In this question, the parenthesis are important. Scale factor changes depending on the direction. When going from a drawing to an actual, scale factor should be > 1. When going from an actual to a drawing, scale factor should be < 1.

Multiple Choice

If I have a scale factor of 1/2, will my picture be larger or smaller after applying the scale factor?

• Larger

• Smaller

Using scale factor

When finding area or perimeter of a shape AND you have a scale factor, do the following:

1. Determine scale factor, if not explicit
2. Scale all dimensions of the shape
3. Solve for area/perimeter.

Ellie is going to a triangular shaped island. She made a map and then she got to know that scale she was using was wrong. She enlarged scale factor to 3cm equals to 15km. Calculate the area of the island using the new scale.

To solve,

1. Find the scale factor:

3 cm = 15 km

Scale factor is 15 km/3cm

Scale factor = 5

To solve,

2 Scale the drawing.

We multiply each part of the triangle by the scale factor of 5.

Multiple Choice

Which of the following show the new lengths of the triangle?

• 16, 16, 24, 20

• 12, 12, 18, 15

• 20, 20, 30, 25

• 24, 24, 36, 30

Finally,

Find the new area using the new dimensions.

A = 1/2 *b*h

Multiple Choice

What is the area of the triangle?

• 250 km^2

• 375 km^2

• 300 km^2

Open Ended

What questions do you have?