4MA0 Higher January 2014 Paper 3R Q21
21
Diagram NOT accurately drawn
The diagram shows a regular pentagon inside a circle, centre \(O\).
The points \(A\) and \(B\) lie on the circle such that \(AB\) is a side of the pentagon.
\(OA = 7\) cm.
\(TA\) is a tangent to the circle and \(OBT\) is a straight line.
Calculate the area of triangle \(ABT\).
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| (\(\angle AOB\) =) 72° | B1 |
\(AT = 7\tan 72^\circ\) or 21.54… or \(OT = \dfrac{7}{\cos 72^\circ}\) or 22.65… | M1 |
| (Area \(\Delta OAT\) =) \(\frac{1}{2} \times 21.54... \times 7\) or (Area \(\Delta OAT\) =) \(\frac{1}{2} \times 7 \times 22.65... \times \sin 72^\circ\) or 75.40… | M1 |
| (Area \(\Delta OAB\) =) \(\frac{1}{2} \times 7 \times 7 \times \sin 72^\circ\) or 23.30… | M1 |
| 52.1 | A1 |
| (5) | |
| (5 marks) |
Notes
B1: May be stated, appear in working or be marked on the diagram
A1: for awrt 52.1