Scale Drawings

Warmup

Activity #1

Scale Drawing of a Playground.

This is a scale drawing of a basketball court. The drawing does not have any measurements labeled, but it says that 1 centimeter represents 2 meters.

• Use this app to help you answer the questions that follow.

• Measure the distances on the scale drawing that are labeled a–d to the nearest tenth of a centimeter.
• Record your results in the first row of the table.

(1.) The statement “1 cm represents 2 m” is the scale of the drawing. It can also be expressed as “1 cm to 2 m,” or “1 cm for every 2 m.” What do you think the scale tells us?

(2.) How long would each measurement from the first question be on an actual basketball court? Explain or show your reasoning.

(3.) On an actual basketball court, the bench area is typically 9 meters long. Without measuring, determine how long the bench area should be on the scale drawing.

(4.) Check your answer by measuring the bench area on the scale drawing. Did your prediction match your measurement?

Activity #2

Assess the Height of a Building by Scaling.

Here is a scale drawing of some of the world’s tallest structures.

• Examine the structures below very closely and answer the questions that follow.

(1.) About how tall is the actual Willis Tower? About how tall is the actual Great Pyramid? Be prepared to explain your reasoning.

(2.) About how much taller is the Burj Khalifa than the Eiffel Tower? Explain or show your reasoning.

(3.) Measure the line segment that shows the scale to the nearest tenth of a centimeter. Express the scale of the drawing using numbers and words.

Activity #3

Assessing the Height of a Building by Scaling.

The Westland Lysander was an aircraft used by the Royal Air Force in the 1930s. Here are some scale drawings that show the top, side, and front views of the Lysander. Use the yellow circle to move the scale, the green circle to rotate the scale, and the slider to increase/reduce length of scale.

• Use the scales and scale drawings to approximate the actual length of the wingspan of the plane, to the nearest foot.

Here below is a scale map of Lafayette Square, a rectangular garden north of the White House.

• Use the inch ruler to measure the line segment of the graphic scale.

About how many feet does one inch represent on this map?

Challenge #1

Challenge #2

FGHIJ is a scaled copy of ABCDE.

Use the applet above to answer the following questions:

(1.) Name the angle in the scaled copy that corresponds to angle BCD.

(2.) Name the segment in the scaled copy that corresponds to segment DE.

(3.) What is the scale factor from polygon ABCDE to polygon FGHIJ?

(4.) A rectangle that is 3 inches by 9 inches is scaled by a factor of 5.

(a.) What are the side lengths of the scaled copy?

(b.) Suppose you want to scale the copy back to its original size. What scale factor should you use?

Challenge #3

Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units.

(1.) How many times larger is the area of of the scaled copy compared to that of Triangle A?

(2.) What scale factor did Lin apply to the Triangle A to create the copy?

(3.) What is the length of bottom side of the scaled copy?

Quiz Time