GCSE Secondary Maths Age 13-17 - Geometry & Measures: Area of irregular shapes - Explained

The video tutorial explains how to solve a geometry problem from a GCSE exam, focusing on calculating the area of a shaded region formed by a trapezium and two semicircles. The instructor guides through the process of finding the area of the trapezium using a formula, then calculating the area of the semicircles by treating them as a full circle. The final step involves subtracting the semicircle area from the trapezium area and rounding the result to three significant figures. The video also highlights the importance of remembering formulas and understanding the allocation of marks for each step.

What is the main objective of the problem involving the trapezium and semicircles?

• To calculate the area of the shaded region

• To find the perimeter of the trapezium

• To find the volume of the trapezium

• To determine the length of the semicircles

Which formula is used to calculate the area of a trapezium?

• Base times height

• Length times width

• Pi times radius squared

• Half the sum of the parallel sides times the height

What is the area of the trapezium in the problem?

• 250 cm²

• 280 cm²

• 300 cm²

• 320 cm²

How do you calculate the area of the two semicircles?

• By adding the diameters of the semicircles

• By subtracting the radius from the diameter

• By finding the area of a full circle

• By finding the area of one semicircle and doubling it

What is the radius of the semicircles in the problem?

• 4 cm

• 5 cm

• 3 cm

• 6 cm

What is the final area of the shaded region rounded to three significant figures?

• 252 cm²

• 250 cm²

• 255 cm²

• 260 cm²

How many marks are awarded for correctly finding the radius?

• One mark

• Two marks

• Four marks

• Three marks