1.

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

Answer»

Area of Triangle (HERON's FORMULA)

Area of Δ = \sqrt{s (s - a) (s - <klux>B</klux>) (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


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