Question

find area of triangle using herons formula if sides are 15cm,15cm,17cm

Answer 1

Area of Triangle (Heron's Formula)

Area of Δ = $\sqrt{s (s - a) (s - b) (s - c)}$

where s (semi-perimeter) =  $\frac{a + b + c}{2}$

Given:

a = b = 15 cm

c = 17 cm

To Find:

Area of Δ

Method:

s = $\frac{a + b + c}{2}$

⇒ s = $\frac{15 + 15 + 17}{2}$

⇒ s = $\frac{47}{2}$

Area of Δ = $\sqrt{\frac{47}{2} (\frac{47}{2} - 15) (\frac{47}{2} - 15) (\frac{47}{2} - 17) }$

⇒ Area =  $\sqrt{\frac{47}{2} (\frac{47 - 30}{2}) (\frac{47 - 30}{2}) (\frac{47 - 34}{2}) }$

⇒ Area = $\sqrt{\frac{47}{2} (\frac{17}{2}) (\frac{17}{2}) (\frac{13}{2}) }$

⇒ Area = $\sqrt{\frac{47}{2} (\frac{17}{2})^{2}(\frac{13}{2}) }$

⇒ Area = $\frac{17}{2} \sqrt{\frac{47}{2} \frac{13}{2} }$

⇒ Area = $\frac{17}{2} \sqrt{\frac{611}{4} }$

⇒ Area = $\frac{17}{4} \sqrt{611}$

⇒ Area = $\frac{17}{4} X 24.718$

⇒ Area = 4.25 X 24.718 cm²

⇒ Area of Triangle = 105.0515 cm²

Answer 2

Answer:

A = 15cm, B = 15cm, C = 17cm

semiperimeter of ∆ ABC, s = (15+15+17)/2 = 47/2 = 23.5

By heron's formula, we know ;

A = √[s (s-a)(s-b)(s-c)]

Hence, A = √[23.5(23.5-15) (23.5-15) (23.5-17)]

A =√[23.5×8.5×8.5×6.5]

A = √11036.1875 cm2

A = 105.0532 cm2

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