Math, asked by reshmakhan5115, 3 months ago

Please help me with this problem of Herons Formula Chapter Help me find the area

Attachments:

Answers

Answered by deepikapatidar402
1

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

Similar questions