# Lesson Worksheet: Calculations with Scale Factors Mathematics

In this worksheet, we will practice finding the perimeter and area of 2D shapes following an enlargement or reduction.

**Q1: **

Benjamin made a drawing for his residence including a villa and a garden, as in the given figure. Using the scale drawing, what is the perimeter of the villa in real life?

**Q2: **

If there is a square whose side length is 9 cm and a triangle whose side lengths are 24 cm each, which of the following statements is correct?

- AThe difference between the perimeter of the square and the perimeter of the triangle is half their sum.
- BThe perimeter of the square is larger than the perimeter of the triangle.
- CThe perimeter of the triangle is twice as long as the perimeter of the square.
- DThe perimeter of the triangle is equal to the perimeter of the square.

**Q3: **

Find the perimeter of a rhombus with a side length of 10 cm after an enlargement with a scale factor of 8.

**Q4: **

Find the area of a square with side length 3 cm after an enlargement with a scale factor of 3.

**Q5: **

Find the perimeter of the following rectangle after an enlargement with a scale factor of 2.

**Q6: **

A rectangle has a width of 36 cm and a length of 60 cm. Find the area of the rectangle after a dilation by scale factor .

**Q7: **

The following figure shows a pair of triangles, where triangle is a new version of triangle after a dilation by scale factor . Find the values of and .

- A and
- B and
- C and
- D and
- E and

Find the perimeter of triangle .

**Q8: **

A picture was enlarged by a scale factor of 10. The resulting pictureβs length was 140 cm and its width was 100 cm. Find the area of the original picture.

**Q9: **

A square of side length 3 cm is enlarged by a scale factor of 2. What is the area of the square after the enlargement?

**Q10: **

Find the perimeter of a regular pentagon whose side length equals 17 cm after an enlargement with a scale factor of 3.