Here is a prism ABCDSPQR - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 3

The area of a trapezium (A) is given by: $A = \frac{1}{2}(a + b)h$ where a and b are the lengths of the parallel sides, and h is the height. Here, a = AB = 14 cm, and CR is given as 12 cm. Let the length of CD = b. We can compute: $147 = \frac{1}{2}(14 + b)h$ We also know from geometry, CR is vertical to AB, making the height h equal to CR = 12 cm. However, we need to check the base length CD using area computation:

Now, to find ST, we can use the Pythagorean theorem considering triangle STC. Using the values obtained: $ST^2 = TC^2 + h^2$ Substituting TC = 6 cm and h = 12 cm: $ST^2 = 6^2 + 12^2\Rightarrow ST^2 = 36 + 144 = 180\Rightarrow ST = \sqrt{180} \approx 13.42 cm$

Using the definition of the tangent in right triangle STC: $\tan(\theta) = \frac{opposite}{adjacent} = \frac{h}{TC} = \frac{12}{6} = 2$ Now solving for angle: $\theta = \tan^{-1}(2) \approx 63.43°$ Thus, the angle between the line ST and the base ABCD is approximately 63.4° when rounded to one decimal place.