Page 12 - Module & More Matematik Tambahan Tg5

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

(b) (c)
O M P A

P
R 1
O
N Q B

Rajah di atas menunjukkan dua sektor, POQ Rajah di atas menunjukkan dua sektor, AOB
dan MON. M ialah titik tengah OP. dan APB. Diberi nisbah jejari OA kepada PA BAB
Ungkapkan α dalam sebutan q jika perimeter ialah 3 : 1, AP = 2 cm dan perimeter rantau
MPQR dan ORN adalah sama. berlorek ialah 10 cm.
The diagram above shows two sectors, POQ and The diagram above shows two sectors, AOB and
MON. M is the midpoint of OP. Express α in terms of APB. Given that the ratio of radius OA to PA is 3 : 1,
q if the perimeter of MPQR and ORN are the same. AP = 2 cm and the perimeter of the shaded region is
10 cm.
Katakan OM = j cm (i) Tunjukkan bahawa q = (5 − 3α) rad:
Let Show that q = (5 − 3α) rad:
Maka, jq + 2j + 2jq = 2j + jα (ii) Jika α = 30°, cari nilai q, dalam radian.
Then, α = 3q If α = 30°, find the value of q, in radian.
(i) Diberi AP = 2 cm, maka OA = 6 cm
6α + 2q = 10
q = 5 − 3α
(ii) α = 30°
π
= rad
6
π
q = 5 − 3  
6
= 3.43 rad
(d) (e)
A K
M
P O - C
3
4 = =
O
B
N L
Rajah di atas menunjukkan satu semibulatan Rajah di atas menunjukkan sektor KOL
berpusat O dan satu sektor berpusat P dan berpusat O dan MLN berpusat L. Diberi bahawa
∠APB = π . Cari jejari PA jika perimeter rantau OM = ML = 5 cm, dan ∠MON = π rad, cari
3 4
berlorek ialah 35π cm. perimeter rantau berlorek itu.
6 The diagram above shows sector KOL with centre O
The diagram above shows a semicircle with centre O and sector MLN with centre L. Given that OM = ML =
π π
and a sector with centre P and ∠APB = . Find the 5 cm, and ∠MON = rad, find the perimeter of the
3 4
radius PA if the perimeter of the shaded region is shaded region.
35π
cm.
6 Perimeter = OM + ON + panjang lengkok MN +
π OA = j MK + panjang lengkok KL + ML
π
3 = 60° 2 = 5 + (5 2 − 5) + 5   + (5 2 − 5) +
4
π
Maka, AP = AB = j. = 35π = πj + πj 5 2   + 5
Then 6 3 2 4
j = 7 cm = 23.62 cm

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