4MA0 Higher June 2016 Paper 3 Q22

22 The diagram shows a pentagon.

Diagram NOT accurately drawn

Work out the area of the pentagon.
Give your answer correct to 3 significant figures.

(6)

Scheme	Marks
\(12^2 + 8^2 - 2 \times 12 \times 8 \times \cos(105)\) (=257...)	M1
257(....) or \(\sqrt{257}\) (=16.05..)	A1
eg. (\(AH\) = ) \(\sqrt{\text{"16.05.."}^2 - 6.5^2}\) (=14.6...) or (\(ADC\) =) \(\cos^{-1}\left(\dfrac{\text{"16.05"}^2 + 13^2 - \text{"16.05"}^2}{2 \times \text{"16.05"} \times 13}\right)\) (=66.08..)	M1
eg. 0.5×12×8×sin(105) (=46.3...) or 12×8×sin(105) (=92.7…) or 0.5×13×"14.6" (=95.4...) or 0.5 × 13 × "16.05" × sin ("66.1")	M1
eg. 2 ×0.5×12×8×sin(105) + 0.5×13×"14.6" or 2×0.5×12×8×sin(105) + 0.5 × 13 × "16.05" × sin ("66.1")	M1
188	A1
	(6)