Please help me with this problem of Herons Formula Chapter Help me find the area
Answers
answer :
Area = 114cm²
step by step explanation :
given
AB = 17cm
CD = 12cm
DA= 9 cm
AC=15cm
BC= ?
In ∆ ADC
perimeter = a+b+c ( a=9 , b= 12 , c= 15 )
P = 9+12+15
P = 36 cm
semiperimeter = perimeter / 2
S = 36 / 2
S = 18 cm
area of triangle ADC by herons formula
Area = √S ( s-a ) ( s-b ) ( s-c )
A = √ 18 (18-9) (18-12) (18-15)
A = √ 18 × 9 × 6 × 3
A = √ 2×3×3×3×3×2×3×3
A = 2 × 3 × 3 × 3
A = 54 centimetre square
In ∆ ABC
by Pythagoras theorem
(17)² = (p)² + (15)²
289 = (p)² + 225
(p)² = 289-225
(p)² = 64
p = √64
p = √2×2×2×2×2×2
p = 2×2×2
p = 8 cm
base = 8 cm
area of triangle = ½×base×height
A = ½×15×8
A = 15 × 4
A = 60 cm²
OR
perimeter of ∆ abc = a+b+c
P = 17+8+15
P = 40 cm
semiperimeter = perimeter / 2
S = 40/2
S = 20 cm
area by herons formula
Area = √ s (s-a) (s-b) (s-c)
A = √ 20 (20-17) (20-8) (20-15)
A = √ 20×3×12×5
A = √ 2×2×5×3×2×2×3×5
A = 2×2×3×5
A = 60 cm²
total area = area of ∆ADc + ∆ABC
A = 54 + 60 cm²
A = 114 cm²