Math Problem Statement

ABCD is a trapezium with the given dimensions.     Calculate the perimeter of the trapezium after an enlargement with the following scale factors:   Scale factor of 2:    cm   Scale factor of 1.5:    cm   Scale factor of 0.5:    cm

Solution

To calculate the perimeter of the trapezium after enlargement, we'll first need to understand how scaling works. When a geometric figure is enlarged by a scale factor, the perimeter is multiplied by that same scale factor.

Let's assume the original perimeter of the trapezium is PP cm. Then, the new perimeter PP' after enlargement will be:

  • For scale factor of 2:
    P=2×PP' = 2 \times P

  • For scale factor of 1.5:
    P=1.5×PP' = 1.5 \times P

  • For scale factor of 0.5:
    P=0.5×PP' = 0.5 \times P

Steps to calculate:

  1. Find the original perimeter PP of the trapezium using its dimensions (if available).
  2. Multiply the original perimeter by the scale factors (2, 1.5, 0.5) to get the new perimeters.

Could you please provide the original dimensions or perimeter of the trapezium? That will allow us to calculate the new values accurately.

Let me know if you have any questions or need more clarification!


Here are 5 related questions:

  1. What is the formula to calculate the perimeter of a trapezium?
  2. How does scaling affect the area of a shape?
  3. If the area of a trapezium is enlarged by a scale factor, how is the area affected?
  4. Can the angles in a trapezium change with scaling? Why or why not?
  5. How do different scale factors impact different types of polygons?

Tip: When working with scale factors, remember that perimeters scale linearly (by the factor), while areas scale by the square of the factor.

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Math Problem Analysis

Mathematical Concepts

Geometry
Scaling
Perimeter

Formulas

Perimeter of a trapezium P = a + b + c + d, where a, b, c, and d are the lengths of the sides
Scaled Perimeter P' = Scale Factor × P

Theorems

Scaling Theorem: Perimeter scales linearly with the scale factor

Suitable Grade Level

Grades 7-9