GCSE Secondary Maths Age 13-17 - Geometry & Measures: Similar Shapes - Explained

The video tutorial explains the concept of mathematically similar trapeziums, focusing on their identical angles and proportional sides. It demonstrates how to calculate the length of a side in a larger trapezium using a scale factor derived from a smaller trapezium. The tutorial also covers finding the area of a shaded region by calculating the area of a larger trapezium and subtracting the area of a smaller one. Key points include understanding the properties of similar shapes, such as angle equality and side ratios.

What is a key characteristic of mathematically similar shapes?

• They have different angles.

• They have identical angles.

• They have different side lengths.

• They have identical areas.

If one side of a smaller trapezium is 12 cm and the corresponding side of a larger trapezium is 18 cm, what is the scale factor?

• 1.2

• 1.5

• 2.0

• 2.5

Given AE = 5 cm in the smaller trapezium, what is the length of AB in the larger trapezium if the scale factor is 1.5?

• 5 cm

• 6.5 cm

• 7.5 cm

• 8 cm

If the area of a smaller trapezium is 36 cm², what is the area of the larger trapezium with a scale factor of 2.25?

• 45 cm²

• 81 cm²

• 90 cm²

• 72 cm²

How do you calculate the area of a larger trapezium if you know the area of a smaller trapezium and the scale factor?

• Multiply the area of the smaller trapezium by the scale factor.

• Multiply the area of the smaller trapezium by the square of the scale factor.

• Divide the area of the smaller trapezium by the scale factor.

• Divide the area of the smaller trapezium by the square of the scale factor.

What is the area of the shaded region if the larger trapezium's area is 81 cm² and the smaller trapezium's area is 36 cm²?

• 45 cm²

• 81 cm²

• 55 cm²

• 36 cm²

What should you remember about similar shapes when solving related problems?

• All areas are the same.

• All angles are the same and all sides are in the same ratio.

• All sides are in different ratios.

• All angles are different.