Answer:
see explanation
Step-by-step explanation:
(a)
the area( A ) of a trapezium is calculated using the formula
A = [tex]\frac{h}{2}[/tex](a + b)
where a and b are the lengths of the parallel sides and h is the perpendicular height between them
here a = 13x, b = 17x + 12 and h = 5
A = [tex]\frac{5}{2}[/tex](13x + 17x + 12) = [tex]\frac{5}{2}[/tex](30x + 12)
A = 5(15x + 6) = 75x + 30 cm²
(b) ΔABC is a right triangle so we can use the sine ratio to solve for y
We require to find BC using Pythagoras' identity
BC² = 5² + 12² = 25 + 144 = 169
⇒ BC = [tex]\sqrt{169}[/tex] = 13, hence
sin y° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{13}[/tex]
⇒ y = [tex]sin^{-1}[/tex]([tex]\frac{5}{13}[/tex]) = 22.6° ( to 1 dec. place )
