Scale Drawings and Similar Figures: math practice, Grade 7 – download the PDF

1 Drawing to real length ★★★

A blueprint uses the scale 1 cm : 4 m. A wall measures 6 cm on the blueprint. What is its actual length?

2 Find the scale factor ★★★

A rectangle is 4 in by 6 in. A copy is 12 in by 18 in. What is the scale factor from the original to the copy?

3 A road map ★★★

On a map, 1 in represents 10 mi. Two cities are 3.5 in apart on the map. How far apart are they in real life?

4 True or false: angles ★★★

Mia says: "If I enlarge a triangle with a scale factor of 2, each angle measure doubles." Is she correct? Explain.

5 Real to drawing ★★★

A soccer field is 50 m wide. A drawing uses the scale 1 cm : 5 m. How wide is the field in the drawing?

6 A model car ★★★

A model car has the scale 1 : 24. The model is 7 in long. How long is the real car in feet? (1 ft = 12 in)

7 Complete the table ★★★

The scale is 1 cm : 3 ft. Copy and complete the table.

8 A bedroom floor plan ★★★

A floor plan uses the scale 1 in : 4 ft. The bedroom measures 2.5 in by 3 in on the plan.

1. Find the actual dimensions.
2. Find the actual area.

9 Similar triangles ★★★

Triangle ABC has sides 6, 8, and 10. Triangle DEF is similar, and its sides are 9, 12, and a third side \( x \). Find \( x \).

10 Kilometers on a map ★★★

A map has the scale 1 cm : 500 m. A trail measures 7.2 cm on the map. How long is the trail in kilometers?

11 Fractional scale ★★★

A drawing uses the scale \( \dfrac{1}{4} \) in = 1 ft. A porch measures 3.5 in on the drawing. How long is the porch?

12 Changing the scale ★★★

A drawing of a courtyard uses the scale 1 cm : 2 m and measures 8 cm by 5 cm. Redraw it with the scale 1 cm : 4 m. What are the new dimensions?

13 Is it a scale drawing? ★★★

A 4 cm by 6 cm rectangle is redrawn as a 6 cm by 8 cm rectangle. Is the second rectangle a scale drawing of the first? Justify.

14 A model of a tower ★★★

A tower is 150 m tall. A model uses the scale 1 : 200. How tall is the model in centimeters?

15 Area of an enlargement ★★★

A 3 cm by 5 cm rectangle is enlarged with a scale factor of 4.

1. Find the area of the original and of the enlargement.
2. By what number was the area multiplied?

16 Area of a lake ★★★

On a map with the scale 1 cm : 5 km, a lake looks like a rectangle 2.4 cm by 1.5 cm. Find the actual area of the lake.

17 A garden plan ★★★

A garden is drawn with the scale 1 cm : 50 cm. Its drawing has an area of 48 cm². Find the actual area in square meters.

18 Find the scale factor from areas ★★★

A rectangle has an area of 36 square inches. A scaled copy has an area of 81 square inches. What is the scale factor from the original to the copy? If the original is 9 in by 4 in, give the dimensions of the copy.

19 Photo enlargement ★★★

A 4 in by 6 in photo is enlarged so that its shorter side becomes 10 in.

1. What is the scale factor?
2. How long is the longer side?
3. How many times larger is the area of the enlargement?

20 Floor of a model house ★★★

The rectangular floor of a model house is 24 cm by 18 cm. The model scale is 1 : 50.

1. Find the actual dimensions in meters.
2. Find the actual floor area in square meters.

21 Perimeter and area of similar triangles ★★★

Triangle ABC is a right triangle with sides 6, 8, and 10. Triangle DEF is similar to ABC with a scale factor of 2.5.

1. Find the sides of DEF.
2. Compare the perimeters of the two triangles.
3. Compare the areas.

22 Which scale is bigger? ★★★

Map X uses the scale 1 cm : 2 km. Map Y uses the scale 1 cm : 5 km. A park is 10 km long. How long is it on each map? Which map shows the park larger, and by what factor?