Building shapes and reading scale drawings

Mathematics · Geometry · ages 11-13

Name ______________________ Date ____________

A rectangle is 4 cm long and 3 cm wide. It is enlarged by a scale factor of 3. How long is the enlarged rectangle?
- 12 cm
- 7 cm
- 9 cm
- 6 cm
Zoe draws a triangle with a 6 cm side, a 4 cm side, and a 30 degree angle between them. She has drawn the 6 cm side. Where does she place her protractor to mark the angle?
- At one end of the 6 cm side, where the 4 cm side will begin
- At the exact middle of the 6 cm side
- At the corner opposite the 6 cm side, where no side has been drawn yet
On a scale drawing, if 1 cm stands for 5 m, a line measuring 3 cm on the drawing represents 15 m in real life.
Circle one: True False
You read a protractor and the pointer sits between the 47 and 48 degree marks, closer to 47. For the tasks in this topic you round to the nearest whole degree. What do you record?
- 47°
- 48°
- 47.5°
A figure has two angles that look almost equal on paper. Your protractor readings are 62° and 65°. What should you trust?
- Your eyes, since the figure looks symmetric
- Neither, guess an average of both angles
- The protractor readings, since angles that look similar can still differ by several degrees
A triangle has a 10 cm side and a 6 cm side. Where must a 20 degree angle sit for the SAS condition to apply?
- At the end of the 10 cm side, away from the 6 cm side
- Between the 10 cm and 6 cm sides
- Opposite the 6 cm side
A small rectangle is 6 cm long and 4 cm wide. A similar big rectangle is 15 cm long. What is the length scale factor from the small rectangle to the big one?
Answer: ______________
A floor plan has a scale of 1 cm = 2 m. A bedroom wall measures 3.5 cm on the plan. How many meters long is the real wall?
Answer: ______________
Ravi read a scale drawing labeled '1 cm to 4 m'. He measured a garden path as 6 cm and calculated the real length as 6 + 4 = 10 m. What went wrong?
- He measured the path in the wrong units
- He added instead of multiplying the measurement by the scale
- He used the wrong ruler, so the measurement was not correct to begin with
To construct a triangle using SAS, given a 7 cm side, a 4 cm side, and a 38 degree included angle, how many separate measurements in total (side lengths plus the angle) must you mark with your ruler and protractor?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

Building shapes and reading scale drawings W1-mt_Jf8xcX4UTq-s1

12 cm · A scale factor of 3 means every length is multiplied by 3, so 4 cm becomes 12 cm.
At one end of the 6 cm side, where the 4 cm side will begin · The 30 degree angle is the included angle, so it must sit between the two given sides. It gets built at an end of the 6 cm side, where the 4 cm side will start.
True · Multiply the ruler length by the scale: 3 times 5 equals 15 m.
47° · Round to the nearest whole degree mark, not to a half degree.
The protractor readings, since angles that look similar can still differ by several degrees · A protractor gives a reading in degrees, rounded to the nearest whole degree for the tasks in this topic. Appearances can be misleading, especially on small drawings.
Between the 10 cm and 6 cm sides · SAS needs the included angle, the one between the two given sides. The 20 degree angle must sit between the 10 cm and 6 cm sides.
2.5 · Divide a matching pair of lengths: 15 / 6 = 2.5, so the length scale factor is 2.5.
7 · Multiply the plan length by the scale: 3.5 times 2 equals 7 m.
He added instead of multiplying the measurement by the scale · Going from a drawing length to a real length needs multiplication, not addition. The real length is 6 times 4, or 24 m.
3 · SAS needs exactly three measurements: the two given side lengths and the one included angle between them.