Question

Hitunglah keliling dan luas bangun yang diarsir berikut ini. pakai caranya! no 12

Answer 1

A) Diketahui :
persegi panjang :
p = 14 cm
l = 21 - 14 cm = 7 cm
* kenapa dikurangi 14 cm? karena yg 14 cm itu punyanya 1/4 lingkaran

L = p × l = 14 × 7 = 98 cm²

1/4 lingkaran : r = 14 cm
L = 1/4 πr² = 1/4 × 22/7 × 14² = 154 cm²

L yg diarsir = L persegi panjang + L 1/4 lingkaran = 98 + 154 = 252 cm²

K = (p + 2l) + r + (1/4 × 2 × π × r)
=(14+ 2(7) ) + 14 + ( 1/4 × 2 × 22/7 × 14)
= 64 cm


b) s = d = 12 cm
r = 6cm

L yg diarsir = L persegi panjang - L (4 × 1/4) lingkaran = s² - (πr²) = 12² - (3,14 × 6²) = 144 - 113,04 = 30,96 cm²

K yg diarsir = K (4 × 1/4) lingkaran = 2πr = 2 × 3,14 × 6 = 37,68 cm

c) persegi panjang :
p = 7 cm
l = 3,5 cm

lingkaran 1 :
d = 3,5 cm
r = 1,75 cm

lingkaran 2 :
d = 7 cm
r = 3,5 cm

L yg diarsir = L persegi panjang + (2 × 1/2 × L lingkaran 1) + (1/2 × L lingkaran 2)
= (p × l) + (1 × πr²) + (1/2 × πr²)
= (7 × 3,5) + (22/7 × 1,75²) + (1/2 × 22/7 × 3,5²)
= 24,5 + 9,625 + 19,25
= 53,375 cm²

K = K (2 × 1/2 lingkaran1) + K (1/2 lingkaran2) + p = (1 × 2πr) + (1/2 × 2πr) + p = (2 × 22/7 × 1,75) + (1/2 × 2 × 22/7 × 3,5) + 7 = 11 + 11 + 7 = 29 cm

d) r = 8 cm
L = 1/2 πr² = 1/2 × 3,14 × 8² = 100,48 cm²
K = (1/2 × 2πr) + (2 × 1/2 πd) = (1 × 3,14 × 8) + ( 3,14 × 8) = 50,28 cm

e) lingkaran1 : d = 21 cm r = 10,5 cm
lingkaran2 : d = 7 cm r = 3,5 cm

L yg diarsir = (1/2 × L lingkaran1) - ( (2 - 1) 1/2 L lingkaran 2)
= (1/2 × 22/7 × 10,5²) - (1/2 × 22/7 × 3,5²)
= 173,25 - 19,25 = 154 cm²

K yg diarsir = (1/2 × K lingkaran1) + (3 × 1/2 lingkaran 2)
= (1/2 × 22/7 × 21) + (3/2 × 22/7 × 7)
= 33 + 33 = 66 cm

f) persegi panjang :
p = 8 cm
l = 6 cm

lingkaran1 :
d = 8cm
r = 4 cm

lingkaran2 :
d = 6 cm
r = 3cm

lingkaran3
r = 3cm

L yg diarsir = (L persegi panjang) + (L 1/2 lingkaran1) + (L 1/2 lingkaran2) - (L1/4 lingkaran3)
= ( p × l ) + (1/2 × πr²) + (1/2 × πr²) - ( 1/4 × πr²)
= ( 8 × 6 ) + ( 1/2 × 3,14 × 4²) + ( 1/2 × 3,14 × 3²) - ( 1/4 × 3,14 × 3²)
= 48 + 25,12 + 14,13 - 7,065
= 80,185 cm²

K yg diarsir = 5 + 3 + (K 1/2 lingkaran1) +(K 1/2 lingkaran2) + (K 1/4 lingkaran3)
= 8 + (1/2 × 3,14 × 8) + (1/2 × 3,14 × 6) + (1/4 × 3,14 × 6)
= 8 + 12,56 + 9,42 + 4,71
= 34,69 cm