4400 Higher November 2004 Paper 4 Q20

EdexcelHigherOld spec7 marksCircles & Sectors

Equilateral triangle ABC of side 8 cm; arcs of radius 4 cm centred at A, B and C meet the sides at P, Q and R; the region between the arcs is shaded

Diagram NOT accurately drawn

\(ABC\) is an equilateral triangle of side 8 cm.
With the vertices \(A\), \(B\) and \(C\) as centres, arcs of radius 4 cm are drawn to cut the sides of the triangle at \(P\), \(Q\) and \(R\).
The shape formed by the arcs is shaded.

(a) Calculate the perimeter of the shaded shape.
Give your answer correct to 1 decimal place. (3)

(b) Calculate the area of the shaded shape.
Give your answer correct to 1 decimal place. (4)

Scheme	Marks
\(\dfrac{60}{360}\) oe or \(\dfrac{180}{360}\) oe seen	B1
\(\dfrac{2\pi \times 4}{2}\)	M1
12.6	A1
	(3)

Mark scheme (b)

Scheme	Marks
eg \(\frac{1}{2} \times 8 \times 8 \times \sin 60^\circ\)	M1
\(\frac{1}{2} \times \pi \times 4^2\)	M1
25.1 or 27.7	A1
2.6	A1
	(4)
	(7 marks)

Notes

M1: for any method of finding Δ area

A1: for one correct evaluation to 3sf or better
27.7 (27.7128…) or 25.1 (25.1327…)

A1: for 2.6 or better (2.580…)