6 The first term of a convergent geometric progression is 10 . The sum of the first 4 terms of the progression is \(p\) and the sum of the first 8 terms of the progression is \(q\). It is given that \(\frac { q } { p } = \frac { 17 } { 16 }\). Find the two possible values of the sum to infinity.
\includegraphics[max width=\textwidth, alt={}, center]{49e137bf-42cc-41af-b5d9-85301d4699b8-08_801_730_255_669} The diagram shows a metal plate \(A B C D E F\) consisting of five parts. The parts \(B C D\) and \(D E F\) are semicircles. The part \(B A F O\) is a sector of a circle with centre \(O\) and radius 20 cm , and \(D\) lies on this circle. The parts \(O B D\) and \(O D F\) are triangles. Angles \(B O D\) and \(D O F\) are both \(\theta\) radians.

1. Given that \(\theta = 1.2\), find the area of the metal plate. Give your answer correct to 3 significant figures.
   \includegraphics[max width=\textwidth, alt={}, center]{49e137bf-42cc-41af-b5d9-85301d4699b8-08_2715_42_110_2006}
2. Given instead that the area of each semicircle is \(50 \pi \mathrm {~cm} ^ { 2 }\), find the exact perimeter of the metal plate.