Math, asked by shravankunhoos7675, 9 months ago

2.If the sides of a triangle are 20cm,24cm and 28cm,find its area *

Answers

Answered by Skyllen
8

 \bf \underline{GIVEN:- } \:  \sf{Sides \: of \: triangles \: are \: 20,24 \: and \: 28cm}.

 \bf \underline{TO \: FIND:-} \:  \sf{Area \: of \: triangle.}

 \bf \underline{SOLUTION:-}

 \sf \: Herons \: formula =  \sqrt{s(s - a)(s - b)(s - c)}

By using Heron's Formula,

 \sf \: S =  \dfrac{Sum \: of \: side}{2}

  \sf  S =  \dfrac{20 + 24 + 28}{2}

 \sf \: S = 36cm

Now,

 \sf \: Area \: of \:  triangle =  \sqrt{36(36 - 20)(36 - 24)(36 - 28)}

 \sf \:  \:  \:  \:  =  \sqrt{36 (16)(12)(8)}

\sf \:  \:  \:  \:  =   \sqrt{36 \times 1536}

\sf \:  \:  \:  \:  =   \sqrt{55296}

\sf \:  \:  \:  \:  =  235.1cm {}^{2}

Therefore, area of triangle is 235.1cm².

_______________________

Heron's formula calculate the area of a triangle with given length of each side. If the length of 3 sides is known, then we can find the area of a triangle through Heron's Formula.

If we're having base and height of triangle, then we can use: 1/2×base×height identity to find its area.

Answered by Thelncredible
2

Given ,

  • The measures of sides of triangle are 20 cm , 24 cm and 28 cm

We know that ,

The semi perimeter of triangle is given by

Semi perimeter (s) = (a + b + c)/2

Thus ,

s = (20 + 24 + 28)/2

s = 72/2

s = 36 cm

Now , the area of triangle is given by

 \boxed{ \sf{Area =  \sqrt{s(s - a)(s - b)(s - c)} }}

Thus ,

Area = √{36(36-20)(36-24)(36-28)}

Area = √{36 × 16 × 12 × 8}

Area = √36 × √16 × √96

Area = 6 × 4 × 2.44

Area = 96 × 2.44

Area = 234.4 cm² (approx)

Therefore ,

  • Thee area of triangle is 234 cm²
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