Hi
Could someone please give me hints 4 the questions circled in the attachment? I have no clue how to start to arrive at those answers.
Thanx a lot.
Hello xwrathbringerx1(a) Let $\displaystyle QR = x$. Then $\displaystyle QP = x\cos\alpha$.
So $\displaystyle x(1+\cos\alpha) = 2$ (= total length of wire)
And $\displaystyle PR = x\sin\alpha$
Then use $\displaystyle A = \tfrac12.PR.QP$
2(a) Draw vertical lines through the top vertices of the trapezium to the base. Then using the right-angled triangles thus formed, the width of the channel across the top is $\displaystyle 4+ 4\cos\theta + 4\cos\theta = 4 + 8\cos\theta$, and the depth of the channel $\displaystyle = 4\sin\theta$.
Then use the formula:
Area of a trapezium =$\displaystyle \tfrac12$(sum of parallel sides) $\displaystyle \times$ (perpendicular distance between them)
$\displaystyle =\tfrac12(4 + 4 + 8\cos\theta)\times 4\sin\theta$
$\displaystyle = ...$
Grandad