4. WMA11/01 Edexcel IAL P1 January 2020, Q4 (Radians: Radian Measure)
Figure 2 shows the plan view of a house ABCD and a lawn APCDA.
ABCD is a rectangle with AB = 16m.
APCOA is a sector of a circle centre O with radius 12m.
The point O lies on the line DC, as shown in Figure 2.
(a) Show that the size of angle AOD is 1.231 radians to 3 decimal places.
(2)
The lawn APCDA is shown shaded in Figure 2.
(b) Find the area of the lawn, in m2, to one decimal place.
(4)
(c) Find the perimeter of the lawn, in metres, to one decimal place.
(3)
SOLUTION
a-
Using trignometric ratios, to find the angle AOD.
b-
Where area of sector is given as
Where
So the area of the sector is
And, the area of triangle AOD is given as
Therefore, the Area of Lawn is given as
c- The perimeter of lawn is the sum of arc length APC, length DC, & length AD.
Where, DC=16m, l=rθ, & AD is
So perimeter of the lawn is
