diketahui persegi ABCD dengan panjang sisi 20 cm. jika panjang CF = 4 cm, luas segitiga ABE adalah...

Kelas 8 Matematika
Bab Bangun Datar

CF = 4 cm

DF = DC - CF
DF = 20 - 4
DF = 16 cm

CF/DF = EC/AD
4/16 = EC/20
EC = 20 . 4/16
EC = 5 cm

BE = BC + EC
BE = 20 + 5
BE = 25 cm

Luas segitiga ABE
= 1/2 . AB . BE
= 1/2 . 20 . (20 + 5)
= 10 . 25
= 250 cm²

ABCD = Persegi dengan ukuran 20 cm
CF = 4 cm

CE/CF = BE/AB
CE/CF = (BC + CE)/AB
CE/4 = (20 + CE)/20
CE × 20 = (20 + CE) × 4
20CE = 80 + 4CE
20CE - 4CE = 80
16CE = 80
CE = 80/16
CE = 5 cm

BE = BC + CE
BE = 20 + 5
BE = 25 cm

L ABE = 1/2 × AB × BE
L ABE = 1/2 × 20 × 25
L ABE = 250 cm^2

Jadi luas segitiga ABE adalah 250 cm^2 (D)